Sherman’s and related inequalities with applications in information theory

Abstract

In this paper we give extensions of Sherman’s inequality considering the class of convex functions of higher order. As particular cases, we get an extended weighted majorization inequality as well as Jensen’s inequality which have direct connection to information theory. We use the obtained results to derive new estimates for Shannon’s and Rényi’s entropy, information energy, and some well-known measures between probability distributions. Using the Zipf–Mandelbrot law, we introduce new functionals to derive some related results.

Refinements of the integral form of Jensen’s and the Lah–Ribarič inequalities and applications for Csiszár divergence

“…In this section, we give some interesting estimates for the integral Csiszár divergence and for its important particular cases (see, e.g., [4,5,9,10,12,15]). , and let a 0 , a 1 , .…”

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”