New Improvements of the Jensen–Mercer Inequality for Strongly Convex Functions with Applications

In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known r...

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Bibliographic Details
Published in:Axioms Vol. 13; no. 8; p. 553
Main Authors: Adil Khan, Muhammad, Ivelić Bradanović, Slavica, Mahmoud, Haitham Abbas
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2024
Subjects:
Convex analysis
convex and strongly convex functions
Convex functions
Inequalities (Mathematics)
Inequality
Information theory
Jensen inequality
Jensen–Mercer inequality
Mathematical optimization
strong f-divergences
Pakistan
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about strongly convex functions. We are also focused on important applications of the derived results in information theory, deducing estimates for χ-divergence, Kullback–Leibler divergence, Hellinger distance, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence. Additionally, we prove some applications to Mercer-type power means at the end.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13080553