Jensen inequality with Applications in Information Theory

Subject Areas : Analyze

hasan barsam ¹ (Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran)
Yamin Sayyari ² (Department of Mathematics, Sirjan University Of Technology, Sirjan, Iran)
sayyed mehrab ramezani 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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