强凸函数的广义詹森和詹森-默塞尔不等式及其应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.