Uniform Treatment of Integral Majorization Inequalities with Applications to Hermite-Hadamard-Fejér-Type Inequalities and f-Divergences

Autor:	László Horváth
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	majorization inequalities convex functions signed measures Hermite-Hadamard-Fejér-type inequalities refinement f-divergences Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 25, Iss 6, p 954 (2023)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e25060954
Popis:	In this paper, we present a general framework that provides a comprehensive and uniform treatment of integral majorization inequalities for convex functions and finite signed measures. Along with new results, we present unified and simple proofs of classical statements. To apply our results, we deal with Hermite-Hadamard-Fejér-type inequalities and their refinements. We present a general method to refine both sides of Hermite-Hadamard-Fejér-type inequalities. The results of many papers on the refinement of the Hermite-Hadamard inequality, whose proofs are based on different ideas, can be treated in a uniform way by this method. Finally, we establish a necessary and sufficient condition for when a fundamental inequality of f-divergences can be refined by another f-divergence.
Databáze:	Directory of Open Access Journals
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