Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences

Ivelić Bradanović, Slavica

doi:10.1016/j.jmaa.2023.127866

Journal of Mathematical Analysis and Applications

2024

DOI: 10.1016/j.jmaa.2023.127866

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Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences

Slavica Ivelić Bradanović

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2024

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Strong $\mathcal {F}$-convexity and concavity and refinements of some classical inequalities

Perić

2024

J Inequal Appl

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The concept of strong ${\mathcal {F}}$ F -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong ${\mathcal {F}}$ F -concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.

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Strong $\mathcal {F}$-convexity and concavity and refinements of some classical inequalities

Perić

2024

J Inequal Appl

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Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences

Cited by 1 publication

References 19 publications

Strong $\mathcal {F}$-convexity and concavity and refinements of some classical inequalities

Strong $\mathcal {F}$-convexity and concavity and refinements of some classical inequalities

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