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A Refinement of the Jensen-Simic-Mercer Inequality with Applications to Entropy

Yamin Sayyari
한국수학교육학회|2022.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제29권 제1호|pp. 51-57|DOI https://doi.org/10.7468/jksmeb.2022.29.1.51

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참고문헌

키워드

Shannon's entropyJensen's inequalitySimic's inequalityMercer's inequalityconvex function.
주제분류수학

초록

The Jensen, Simic and Mercer inequalities are very important inequalities in theory of inequalities and some results are devoted to this inequalities. In this paper, firstly, we establish extension of Jensen-Simic-Mercer inequality. After that, we investigate bounds for Shannon’s entropy of a probability distribution. Finally, We give some new applications in analysis.

Abstract

The Jensen, Simic and Mercer inequalities are very important inequalities in theory of inequalities and some results are devoted to this inequalities. In this paper, firstly, we establish extension of Jensen-Simic-Mercer inequality. After that, we investigate bounds for Shannon’s entropy of a probability distribution. Finally, We give some new applications in analysis.

참고문헌 (18)

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