Generalized Jensen and Jensen–Mercer inequalities for strongly convex functions with applications

Strongly convex functions as a subclass of convex functions, still equipped with stronger properties, are employed through several generalizations and improvements of the Jensen inequality and the Jensen–Mercer inequality. This paper additionally provides applications of obtained main results in the...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2024; no. 1; pp. 112 - 19
Main Authors: Ivelić Bradanović, Slavica, Lovričević, Neda
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 02.09.2024
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Chebyshev approximation
Chebyshev functional
Convex analysis
Convex and strongly convex functions
Entropy (Information theory)
Estimates
Inequalities
Inequality
Jensen inequality
Jensen–Mercer inequality
Mathematics
Mathematics and Statistics
Strong f-divergences
94A15
26D20
Jensen–Mercer inequality
Chebyshev functional
Convex and strongly convex functions
94A17
divergences
Jensen inequality
Strong
26D15
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:Strongly convex functions as a subclass of convex functions, still equipped with stronger properties, are employed through several generalizations and improvements of the Jensen inequality and the Jensen–Mercer inequality. This paper additionally provides applications of obtained main results in the form of new estimates for so-called strong f -divergences: the concept of the Csiszár f -divergence for strongly convex functions f , together with particular cases (Kullback–Leibler divergence, χ 2 -divergence, Hellinger divergence, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence.) Furthermore, new estimates for the Shannon entropy are obtained, and new Chebyshev-type inequalities are derived.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03189-z