On generalization of Mercer’s inequality involving averages of convex functions

Utilizing integral arithmetic mean and applying a generalized form of Niezgoda?s inequality, we present new proofs concerning the (m,n)-convexity of the integral arithmetic mean function, denoted as F. Additionally, we establish an inequality for divided differences by employing the extended form of...

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Bibliographic Details
Published inApplicable analysis and discrete mathematics p. 12
Main Authors Aras-Gazic, Gorana, Pecaric, Josip, Praljak, Marjan
Format Journal Article
LanguageEnglish
Published 2025
Online AccessGet full text
ISSN1452-8630
2406-100X
DOI10.2298/AADM231206012A

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Summary:Utilizing integral arithmetic mean and applying a generalized form of Niezgoda?s inequality, we present new proofs concerning the (m,n)-convexity of the integral arithmetic mean function, denoted as F. Additionally, we establish an inequality for divided differences by employing the extended form of Niezgoda?s inequality. Moreover, we demonstrate the convexity of the function defined by these divided differences.
ISSN:1452-8630
2406-100X
DOI:10.2298/AADM231206012A