Authors: Simić, Slavko 
Todorčević, Vesna 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities
Journal: Mathematics
Volume: 9
Issue: 23
First page: 3104
Issue Date: 1-Dec-2021
Rank: ~M21a
ISSN: 2227-7390
DOI: 10.3390/math9233104
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.
Keywords: quasi-arithmetic means | power means | convex functions | Hölder’s inequality
Publisher: MDPI

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