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

Slavko Simić and Vesna Todorčević
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Slavko Simić: Mathematical Institute SANU, 11000 Belgrade, Serbia
Vesna Todorčević: Mathematical Institute SANU, 11000 Belgrade, Serbia

Mathematics, 2021, vol. 9, issue 23, 1-12

Abstract: In this article, we give sharp two-sided bounds for the generalized Jensen functional J n ( f , g , h ; p , x ). Assuming convexity/concavity of the generating function h , we give exact bounds for the generalized quasi-arithmetic mean A n ( 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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