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Inequalities for averages of quasiconvex and superquadratic functions
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2016 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 2, p. 535-550Article in journal (Refereed) Published
Abstract [en]

For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

Place, publisher, year, edition, pages
2016. Vol. 19, no 2, p. 535-550
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-10062DOI: 10.7153/mia-19-40ISI: 000374170300009Scopus ID: 2-s2.0-84958824735Local ID: 8d020a5b-4ec5-47c7-b999-5644a2b10659OAI: oai:DiVA.org:ltu-10062DiVA, id: diva2:983002
Note
Validerad; 2016; Nivå 2; 20160302 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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