强凸函数的广义詹森和詹森-默塞尔不等式及其应用

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-09-02 DOI:10.1186/s13660-024-03189-z

Slavica Ivelić Bradanović, Neda Lovričević

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引用次数: 0

摘要

强凸函数作为凸函数的一个子类，仍然具有更强的性质，通过对詹森不等式和詹森-默塞尔不等式的几种概括和改进而得到应用。本文还以所谓强 f 发散的新估计的形式提供了所获主要结果的应用：强凸函数 f 的 Csiszár f 发散概念以及特殊情况（Kullback-Leibler 发散、$chi ^{2}$ -发散、Hellinger 发散、Bhattacharya 距离、Jeffreys 距离和 Jensen-Shannon 发散）。此外，还得到了香农熵的新估计值，并推导出新的切比雪夫型不等式。

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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 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, $\chi ^{2}$ -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.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.