Jensen inequality with Applications in Information Theory

Subject Areas : Analyze

hasan barsam ¹ , Yamin Sayyari ² , sayyed mehrab ramezani ³

1 - Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran
2 - Department of Mathematics, Sirjan University Of Technology, Sirjan, Iran
3 - Faculty of Technology and Mining, Yasouj University, Choram, Iran

Received: 2021-10-30 Accepted : 2023-01-31 Published : 2023-08-01

Keywords: واگرایی سیزار, نامساوی ینسن, آنتروپی شانون, میانگین ها, کران های عمومی,

Abstract :

One of the best-known inequalities which are used in many inequities is Jensen’s inequality. It is a base of some inequality such as the arithmetic mean, harmonic mean inequality also in inequality with respect to entropies including Shannon’s inequality and information theory. One of the best fundamental inequality in mathematics is Jensen’s inequality. In fact, Jensen's inequality is a base of some inequality such as the arithmetic mean, harmonic mean inequality also in inequality with respect to entropies including Shannon’s inequality, Ky Fan’s inequality and etc. Recently, the generalizations and refinement for the Jensen inequality have been considered by many authors, it has been generalized to applications of information theory and etc. The purpose of this research article is to give a new interesting refinement of Jensen’s inequality form particular finite sequences. Also, we give some applications with respect to this inequality in information theory and other aspect of sciences.

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