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• 201.
Narvik University College and Norut Narvik.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Hardy Type Operators in Local Vanishing Morrey Spaces on Fractal Sets2015In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 18, no 5, p. 1252-1276Article in journal (Refereed)

We obtain two-weighted estimates for the Hardy type operators fromlocal generalized Morrey spaces Lp,ϕloc (X,w1) defined on an arbitrary underlyingquasi-metric measure space (X, μ, ) with the growth condition, toLq,ψloc (X,w2), where w1 = w1[(x, x0)], x0 ∈ X is a weight of radial type,while w2 = w2(x) may be an arbitrary weight. The proof allows to simultaneouslytreat a similar boundedness V Lp,ϕloc (X,w1) → V Lq,ψloc (X,w2) forvanishing Morrey spaces. We obtain sufficient conditions for such estimatesin terms of some integral inequalities imposed on ϕ, ψ and w1.w2. We alsospecially treat the one weight case where w2(x) is also of radial type. Wedo not impose doubling condition on the measure μ, but base our result onthe growth condition.The obtained results show the explicit dependence of the mapping propertiesof the Hardy type operators on the fractional dimension of the set(X, μ, ). An application to spherical Hardy type operators is also given.

• 202.
Narvik University College and Norut Narvik.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Universidade do Algarve, FCT, Campus de Gambelas, Instituto Superior Tecnico, Research center CEAF. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some sharp inequalities for multidimensional integral operators with homogenous kernel: an overview and new results2016In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 2, p. 551-564Article in journal (Refereed)

One goal of this paper is to point out the fact that a big number of inequalities provedfrom time to time in journal publications, both one-dimensional and multi-dimensional, are particularcases of some general results for integral operators with homogeneous kernels, includingin particular, the statements on sharp constants.Some new multidimensional Hardy-Hilbert type inequalities are derived. Moreover, anew multidimensional P´olya-Knopp inequality is proved and some examples of applications arederived from this result. The constants in all inequalities are sharp.

• 203.
Narvik University College and Norut Narvik, UiT, The Arctic University of Norway, Narvik.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Universidade do Algarve, FCT, Campus de Gambelas, Universidade do Algarve, Faro.
Some sharp inequalities for integral operators with homogeneous kernel2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, article id 114Article in journal (Refereed)

One goal of this paper is to show that a big number of inequalities for functions in L p (R + ) Lp(R+), p≥1 p≥1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0<p

• 204.
Narvik University College and Norut Narvik.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Departamento de Matematica, Universidade do Algarve.
Weighted Hardy operators in complementary Morrey spaces2012In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965Article in journal (Refereed)

We study the weighted p -> q-boundedness of the multidimensional weighted Hardy-type operators H-omega(alpha) and H-omega(alpha) with radial type weight omega = omega(vertical bar x vertical bar), in the generalized complementary Morrey spaces (C) L-(0)(p,psi) (R-n) defined by an almost increasing function psi = psi(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed on psi and omega, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function psi and the weight omega are power functions. We also prove that the spaces (C) L-(0)(p,psi) (Omega) over bounded domains Omega are embedded between weighted Lebesgue space L-p with the weight psi and such a space with the weight psi, perturbed by a logarithmic factor. Both the embeddings are sharp

• 205.
Narvik University College and Norut Narvik.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Universidade do Algarve, FCT, Campus de Gambelas. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Weighted Hardy-type inequalities in variable exponent Morrey-type spaces2013In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, article id 716029Article in journal (Refereed)

We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by p, alpha, and phi, the belongness of which to the resulting space L-q(.),L-psi(.)(R-n, w) is sufficient for such a boundedness. Under additional assumptions on phi/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions phi and phi/w.

• 206. Lukkassen, Dag
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On some sharp bounds for the homogenized p-Poisson equation1995In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 58, no 1, p. 123-135Article in journal (Refereed)
• 207.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some engineering and mathematical aspects on the homogenization method1994In: Proceedings of the International Conference on Composites Engineering ICCE/1 / [ed] David Hui, 1994, p. 903-904Conference paper (Refereed)
• 208. Lukkassen, Dag
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some engineering and mathematical aspects on the homogenization method1995In: Composites Engineering, ISSN 0961-9526, Vol. 5, p. 337-343Article in journal (Refereed)
• 209. Lukkassen, Dag
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On some bounds for the effective conductivity1994In: Proceedings, 1st International Conference on Composites Engineering: ICCE/1 / [ed] David Hui, 1994, p. 855-856Conference paper (Refereed)
• 210.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematics, Sofia University. Department of Mathematics, University of Athens, Panepistimiopolis.
On n-th James and Khintchine constants of Banach spaces2008In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 11, no 1, p. 1-22Article in journal (Refereed)

For any Banach space X the n-th James constants J(n)(X) and the n-th Khintchine constants K-p,q(n)(X) are investigated and discussed. Some new properties of these constants are presented. The main result is an estimate of the n-th Khintchine constants K-p,q(n)(X) by the n-th James constants Jn (X). In the case of n = 2 and p = q = 2 this estimate is even stronger and improvs an earlier estimate proved by Kato-Maligranda-Takahashi

• 211.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
L.N. Gumilyov Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On Hardy q-inequalities2014In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 64, no 3, p. 659-682Article in journal (Refereed)

Some $q$-analysis variants of Hardy type inequalities of the form \int_0^b \bigg(x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_q t \bigg)^{\!p} d_q x \leq C \int_0^b f^p(t) d_q t with sharp constant $C$ are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.

• 212. Maligranda, Lech
Department of Mathematics, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On some inequalities of the Grüss-Barnes and Borell type1994In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 187, no 1, p. 306-323Article in journal (Refereed)

Some new generalizations of the Grüss-Barnes and Borell inequalities are proved. A new proof, using the classical Chebyshev inequality, for the case of two functions is presented and applied. A crucial inequality for $n$ functions by C. Borell \ref[J. Math. Anal. Appl. 41 (1973), 300--312; MR0315073 (47 \#3622)] is also discussed. Some recent results are sharpened and complemented. Interpolated or weighted versions of some of the inequalities are pointed out.

• 213. Maligranda, Lech
Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Stolarsky's inequality with general weights1995In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 123, no 7, p. 2113-2118Article in journal (Refereed)

Recently Stolarsky proved that the inquality ( ) holds for every 0\$" type="#_x005F_x0000_t75">and every nonincreasing function on [0, 1] satisfying . In this paper we prove a weighted version of this inequality. Our proof is based on a generalized Chebyshev inequality. In particular, our result shows that the inequality holds for every function g of bounded variation. We also generalize another inequality by Stolarsky concerning the -function.

• 214. Maligranda, Lech
Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Weighted Favard and Berwald inequalities1995In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 190, no 1, p. 248-262Article in journal (Refereed)

Weighted versions of the Favard and Benwald inequalities are proved in the class of monotone and concave (convex) functions. Some necessary majorization estimates and a double-weight characterization for a Favard-type inequality are included.

• 215. Maligranda, Lech
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Generalized duality of some Banach function spaces1989In: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 51, no 3, p. 323-338Article in journal (Refereed)
• 216.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Inequalities and interpolation: third International Conference "Function Spaces" (Poznan, 1992)1993In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 44, no 1, p. 181-199Article in journal (Refereed)

It is well known that real as well as complex interpolation is closely related to corresponding inequalities for functions, sequences, operators, s-numbers, etc. The present paper is a survey about this interrelation. The list of references contains 66 items. The authors prove classical and more recent inequalities via interpolation techniques in a rather systematic way.

• 217. Maligranda, Lech
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On Clarkson´s inequalities and interpolation1992In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 155, p. 187-197Article in journal (Refereed)
• 218.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Real interpolation between weighted Lp and Lorentz spaces1987In: Polish Academy of Sciences. Bulletin. Mathematics, ISSN 0239-7269, Vol. 35, no 11, p. 765-778Article in journal (Refereed)
• 219. Maligranda, Lech
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Wladyslaw Orlicz (1903-1990)1991In: Notices of the American Mathematical Society, ISSN 0002-9920, E-ISSN 1088-9477, Vol. 38Article in journal (Other (popular science, discussion, etc.))
• 220. Maligranda, Lech
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, Narvik university of technology.
Interpolation and partial differential equations1994In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 35, no 9, p. 5035-5046Article in journal (Refereed)

One of the main motivations for developing the theory of interpolation was to apply it to the theory of partial differential equations (PDEs). Nowadays interpolation theory has been developed in an almost unbelievable way {see the bibliography of Maligranda [Interpolation of Operators and Applications (1926-1990), 2nd ed. (Luleå University, Luleå, 1993), p. 154]}. In this article some model examples are presented which display how powerful this theory is when dealing with PDEs. One main aim is to point out when it suffices to use classical interpolation theory and also to give concrete examples of situations when nonlinear interpolation theory has to be applied. Some historical remarks are also included and the relations to similar results are pointed out

• 221.
Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest.
Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, University of Bucharest and Institute of Mathematics of Romanian Academy.
Schur multiplier characterization of a class of infinite matrices2010In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 60, no 1, p. 183-193Article in journal (Refereed)

Let B w (ℓ p ) denote the space of infinite matrices A for which A(x) ∈ ℓ p for all x = {x k } k=1∞ ∈ ℓ p with |x k | ↘ 0. We characterize the upper triangular positive matrices from B w (ℓ p ), 1 < p < ∞, by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.

• 222.
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Besov-Schatten spaces2012In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 2012Article in journal (Refereed)

We introduce the Besov-Schatten spaces B(p)(l(2)), a matrix version af analytic Besov space, and we compute the dual of this space showing that it coincides with the matricial Bloch space introduced previously in Popa (2007). Finally we compute the space of all Schur multipliers on B(1)(l(2)).

• 223.
Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Simion Stoilov Institute of Mathematics, Romanian Academy, Romania & Technical University, University of Bucharest and Institute of Mathematics of Romanian Academy.
Some new characterizations of Bloch type spaces of infinite matrices via Schur multipliers2015In: Publicationes mathematicae (Debrecen), ISSN 0033-3883, E-ISSN 2064-2849, Vol. 87, no 3-4, p. 351-370Article in journal (Refereed)

We consider the innite matrix version B(D, ℓ2) of the Bloch space. In this paperwe complement the results in the recent book [18] by deriving some new characteriza-tions of B(D, ℓ2) and related spaces and duals via Schur multipliers. As applicationswe nd the largest solid subspace of B(D, ℓ2) and its \conjugate" space I(ℓ2) consid-ered in [18] and [19].

• 224.
Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On a class of linear operators on lp and its Schur multipliers2016In: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 17, no 2, p. 101-108Article in journal (Refereed)

In this paper we consider the spaces , , of infinite matrices defined by the norm . We consider the Schur product of matrices and prove that is not closed under this product. Moreover, we prove that linear and bounded operators on are Schur multipliers on , a result which is not obvious, since is not a Schur algebra. Most of the results are sharp in the sense that they are given via necessary and sufficient conditions. ( ) p w B 1p   A 1 ( ) =1 =1 1 0 := sup p p p jk k B j k w x p xk A a x            ( ) p w B p ( ) p w B ( ) p w B

• 225.
Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Technical University of Civil Engineering Bucharest. University of Bucharest and Institute of Mathematics of Romanian Academy.
A new characterization of Bergman-Schatten spaces and a duality result2009Report (Other academic)
• 226.
Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Technical University of Civil Engineering Bucharest. University of Bucharest and Institute of Mathematics of Romanian Academy.
A new characterization of Bergman-Schatten spaces and a duality result2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 360, no 1, p. 67-80Article in journal (Refereed)

Let B0 (D, ℓ2) denote the space of all upper triangular matrices A such that limr → 1- (1 - r2) {norm of matrix} (A * C (r))′ {norm of matrix}B (ℓ2) = 0. We also denote by B0, c (D, ℓ2) the closed Banach subspace of B0 (D, ℓ2) consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between B0, c (D, ℓ2) and the Bergman-Schatten spaces La1 (D, ℓ2). We also give a characterization of the more general Bergman-Schatten spaces Lap (D, ℓ2), 1 ≤ p < ∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, Lp-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219-237] for classical Bergman spaces.

• 227.
Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On a new space of infinite matrices2013In: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 14, no 4, p. 269-275Article in journal (Refereed)

In this paper we introduce and study some properties for a new class of linear operators namely Bv w(l2). We characterize some special classes of this kind of matrices and we prove some new results concerning Schur multipliers. In particular, we prove that the space of Schur multipliers from Bv w(l2) to B v w(l2) contains all matrices which represent bounded operators from l2 into l∞.

• 228.
Narvik University College, 8505 Narvik, Norway.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On optimal design of two phase materials by using homogenization1997In: Proceedings of the Fourth International Conference on Composites Engineering: ICCE/4 / [ed] David Hui, 1997, p. 653-654Conference paper (Refereed)
• 229.
Department of mathematics, University of Sarajevo.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients2016In: Studia scientiarum mathematicarum Hungarica (Print), ISSN 0081-6906, E-ISSN 1588-2896, Vol. 53, no 4, p. 545-556Article in journal (Refereed)

In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H1/(1+α) to the space L1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

• 230. Mitrinovic, D. S.
Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On a general inequality with applications1992In: Zeitschrift für Analysis und ihre Anwendungen, ISSN 0232-2064, E-ISSN 1661-4534, Vol. 11, no 2, p. 285-290Article in journal (Refereed)
• 231.
Ferdowsi University Mashhad, Centre of Excellence in Analysis on Algebraic Structures, Department of Pure Mathematics, Mashhad.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Reverse Cauchy-Schwarz inequalities for positive C*-valued sesquilinear forms2009In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 12, no 4, p. 701-709Article in journal (Refereed)

We prove two new reverse Cauchy-Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy-Schwarz inequality due to G. Polya and G. Szego

• 232.
Department of General Studies, Dar es Salaam Institute of Technology.
Department of Scientific Computing, Uppsala University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Modeling and simulation of run-up waves on a sloping beach extended with artificial bottom2006Report (Other academic)
• 233. Myasnikov, E.A.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On the best constants in certain integral inequalities for monotone functions1994In: Acta Scientarum Mathematicarum, ISSN 0001-6969, Vol. 59, no 3-4, p. 613-624Article in journal (Refereed)
• 234.
Luleå tekniska universitet.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk.
On weighted inequalities with geometric mean operator generated by the Hardy-type integral transform2002In: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 3, no 4, article id 48Article in journal (Refereed)
• 235.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convex Functions and Their Applications: A Contemporary Approach2018Book (Refereed)

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics.  The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples.  Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.

This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications.

• 236. Niculescu, Constantin P.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Convex functions: basic theory and applications2003Book (Other academic)
• 237.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convex Functions on a Normed Linear Space2018In: Duality and Convex Optimization, Cham: Springer, 2018, p. 107-184Chapter in book (Refereed)

Convex functions and their relatives are ubiquitous in a large variety of applications such as optimization theory, mass transportation, mathematical economics, and geometric inequalities related to isoperimetric problems. This chapter is devoted to a succinct presentation of their theory in the context of real normed linear spaces, but most of the illustrations will refer to the Euclidean space RN,">RN,RN, the matrix space MN(R)">MN(R)MN(R) of all N&#x00D7;N">N×NN×N-dimensional real matrices (endowed with the Hilbert–Schmidt norm or with the operator norm), and the Lebesgue spaces Lp(RN)">Lp(RN)Lp(RN) with p&#x2208;[1,&#x221E;]">p∈[1,∞]p∈[1,∞].

• 238.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convex Functions on Intervals2018In: Duality and Convex Optimization, Cham: Springer, 2018, p. 1-70Chapter in book (Refereed)

The study of convex functions of one real variable offers an excellent glimpse of the beauty and fascination of advanced mathematics. The reader will find here a large variety of results based on simple and intuitive arguments that have remarkable applications. At the same time they provide the starting point of deep generalizations in the setting of several variables, that will be discussed in the next chapters.

• 239.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convex Sets in Real Linear Spaces2018In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 71-106Chapter in book (Refereed)

The natural domain for a convex function is a convex set. In this chapter we review some basic facts, necessary for a deep understanding of the concept of convexity in real linear spaces. For reader’s convenience, all results concerning the separation of convex sets in Banach spaces are stated in Section 2.2 with proofs covering only the particular (but important) case of Euclidean spaces. Full details in the general case are to be found in Appendix  B

• 240.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convexity and Majorization2018In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 185-226Chapter in book (Refereed)

This chapter is aimed to offer a glimpse on the majorization theory and the beautiful inequalities associated to it. Introduced by G. H. Hardy, J. E. Littlewood, and G. Pólya (Messenger Math. 58:145–152, (1929), [208]) in 1929, and popularized by their celebrated book on Inequalities (Hardy et al., Inequalities, Cambridge University Press, 1952, [209]), the relation of majorization has attracted along the time a big deal of attention not only from the mathematicians, but also from people working in various other fields such as statistics, economics, physics, signal processing, data mining, etc. Part of this research activity is summarized in the 900 pages of the recent book by A. W. Marshall, I. Olkin, and B. Arnold (Inequalities: theory of majorization and its applications. Springer, New York (2011), [305]).

• 241.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convexity and Majorization2018In: Duality and Convex Optimization, Cham: Springer, 2018, p. 255-300Chapter in book (Refereed)

Convex optimization is one of the main applications of the theory of convexity and Legendre–Fenchel duality is a basic tool, making more flexible the approach of many concrete problems. The diet problem, the transportation problem, and the optimal assignment problem are among the many problems that during the Second World War and immediately after led L. Kantorovich, T. C. Koopmans, F. L. Hitchcock, and G. B. Danzig to develop the mathematical theory of linear programming. Soon it was realized that most results extend to the framework of convex functions, which marked the birth of convex programming. Later on, W. Fenchel, R. T. Rockafellar, and J. J. Moreau laid the foundations of convex analysis.

• 242.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Convexity in Spaces of Matrices2018In: Duality and Convex Optimization, Cham: Springer, 2018, p. 227-254Chapter in book (Refereed)

In this chapter we investigate three subjects concerning the convexity of functions defined on a space of matrices (or just on a convex subset of it). The first one is devoted to the convex spectral functions, that is, to the convex functions F:Sym(n,R)&#x2192;R">F:Sym(n,R)→RF:Sym(n,R)→R whose values F(A) depend only on the spectrum of A. The main result concerns their description as superpositions f&#x2218;&#x039B;">f∘Λf∘Λ between convex functions f:Rn&#x2192;R">f:Rn→Rf:Rn→R invariant under permutations, and the eigenvalues map &#x039B;">ΛΛ.

• 243.
University of Craiova, Department of Mathematics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Old and new on the Hermite-Hadamard inequality2003In: Real Analysis Exchange, ISSN 0147-1937, E-ISSN 1930-1219, Vol. 29, no 2, p. 663-685Article in journal (Refereed)

The goal of this paper is to describe the panorama of Mathematics grown up from the celebrated inequality of Hermite and Hadamard. Both old and new results are presented, complemented and discussed within this framework.

• 244.
Department of Mathematics, University of Craiova .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .
Special Topics in Majorization Theory2018In: Duality and Convex Optimization, Cham: Springer, 2018, p. 301-326Chapter in book (Refereed)

The primary aim of this chapter is to discuss the connection between the Hermite–Hadamard double inequality and Choquet’s theory. Noticed first by Niculescu (Math Inequal Appl 5(3):479–489, 2002, [356]), Niculescu (Math Inequal Appl 5(4):619–623, 2002, [357]) (during the conference Inequalities 2001, in Timişoara), this connection led him to a partial extension of the majorization theory beyond the classical case of probability measures, using the so-called Steffensen–Popoviciu measures. Their main feature is to offer a large framework under which the Jensen–Steffensen inequality remains available. As a consequence, one obtains the extension of the left-hand side of Hermite–Hadamard double inequality to a context involving signed Borel measures on arbitrary compact convex sets. A similar extension of the right-hand side of this inequality is known only in dimension 1, the higher dimensional case being still open.

• 245.
Department of Mathematics, University of Craiova.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Convex functions and their applications: a contemporary approach2006Book (Other academic)
• 246.
Department of Mathematics, University of Sofia.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Interpolation of nonlinear operators between families of Banach spaces1993In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 72, p. 47-60Article in journal (Refereed)
• 247.
Department of Mathematics, Kliment Ohridski University of Sofia.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some properties of Xp-spaces1991In: Function spaces: Proceedings of the 2nd international conference, Poznan, Poland, August 28-September 2, 1989 / [ed] Julian Musielak; Henry Hudzik; Ryszard Urbanski, Stuttgart: Teubner , 1991, p. 174-185Conference paper (Refereed)
• 248.
Department of Mathematics, Kliment Ohridski University of Sofia, Department of Mathematics and Informatics, Sofia University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, University of Zagreb, University of Zagreb.
Continuous Forms of Classical Inequalities2016In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 13, no 5, p. 3483-3497Article in journal (Refereed)

The main aim of this paper is to focus on the question to develop classical inequalities to hold in a more general “continuous” form (involving infinitely many functions and/or spaces). First, we discuss such developments concerning Hölder’s and Minkowski’s inequalities. After that we present such new general developments of Popoviciu’s and Bellman’s inequalities. Finally, we present some applications, possible extensions and questions for further research.

• 249.
Department of Mathematics and Informatics, Sofia University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, University of Zagreb.
The Beckenbach-Dresher inequality in the psi-direct sums of spaces and related results2012In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, no 1Article in journal (Refereed)

Let ~ A : [0; 1] ! R be a concave function with ~ A(0) = ~ A(1) = 1. There is a corresponding map k:k ~ A for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the Beckenbach{Dresher type inequality connected with A-direct sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions A!;q and k:k!;q , (0 < ! < 1; q < 1) related to the Lorentz sequence space. Other posibilities for parameters ! and q are considered, the inverse HAolder inequalities and more variants of the Beckenbach{Dresher inequalities are obtained.

• 250.
Department of Mathematics, Kliment Ohridski University of Sofia.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On interpolation between Xp -spaces1989In: Function spaces, differential operators and nonlinear analysis: Proceedings of the Summer School of Function Spaces, Differential Operators, and Nonlinear Analysis ... held in Sodankylä, Finnish Lapland, in August 1988 / [ed] Lassi Päivärinta, Harlow: John Wiley & Sons, 1989, p. 89-107Conference paper (Refereed)
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