Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 2021 Serbia English Publisher:MDPI AGJournal:Mathematics, volume 9, page 3,104 (eissn: 2227-7390,

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Authors: Slavko Simić; Vesna Todorčević;

doi: 10.3390/math9233104

Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

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Abstract

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained.

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Serbia

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Keywords

quasi-arithmetic means, convex functions, Holder's inequality, QA1-939, Hölder’s inequality, power means, Mathematics

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