Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions

The well-known Jensen inequality and Hermite-Hadamard inequality were extended using iterated integrals by Z. Retkes in 2008 and then by P. Krus in 2019.In this paper, we consider analytical convex (concave) functions in order to obtain new refinements of Jensen's inequality.We apply the main result to the classical HM-GM-AM, AM-RMS, triangle inequalities and present an application to the geometric series.We also give Mercer type variants of Jensen's inequality.

Publication Details

Journal
SZTE Publicatio Repozitórium (University of Szeged)
Published
2025-01-01
Primary Topic
Mathematical Inequalities and Applications
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article
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article

Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions

SZTE Publicatio Repozitórium (University of Szeged)
Mathematical Inequalities and Applications
article

Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions

article en

Abstract

The well-known Jensen inequality and Hermite-Hadamard inequality were extended using iterated integrals by Z. Retkes in 2008 and then by P. Krus in 2019.In this paper, we consider analytical convex (concave) functions in order to obtain new refinements of Jensen's inequality.We apply the main result to the classical HM-GM-AM, AM-RMS, triangle inequalities and present an application to the geometric series.We also give Mercer type variants of Jensen's inequality.

SZTE Publicatio Repozitórium (University of Szeged)
Reduced inequalities
Openalex Percentile: Top 38%
Mathematical Inequalities and Applications
Open Access PDFOpenAlex
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Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions · SZTE Publicatio Repozitórium (University of Szeged) (2025) | TGRS Research Map | TGRS