Refinement of the classical Jensen inequality using finite sequences

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2024-01-10 DOI:10.15672/hujms.1270585

Z. M. M. M. Sayed, M. Adil Khan, Shahid Khan, J. Pečarić

引用次数: 0

Abstract

This article is dedicated to a refinement of the classical Jensen inequality by virtue of some finite real sequences. Inequalities for various means are obtained from this refinement. Also, from the proposed refinement, the authors acquired some inequalities for Csisz\^{a}r $\Psi$- divergence and for Shannon and Zipf-Mandelbrot entropies. The refinement is further generalized through several finite real sequences.

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利用有限序列完善经典詹森不等式

本文致力于通过一些有限实数序列来完善经典的詹森不等式。从这一改进中得到了各种手段的不等式。此外，作者还从提出的细化中获得了 Csisz\^{a}r $\Psi$- 发散以及香农和齐普夫-曼德尔布罗特熵的一些不等式。通过几个有限实数序列进一步推广了该细化方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.