Shannon Type Inequalities for Kapur’s Entropy

Abstract

In the paper, by methods of the theory of majorization, the authors establish the Schur m-convexity and Shannon type inequalities for Kapur’s entropy.

On HT-convexity and Hadamard-type inequalities

“…In this section, we will consider applications of our newly-established results to the following special means. For real numbers τ , μ > 0, the arithmetic mean and the p-logarithmic mean are respectively defined [26,29]…”

Generalizations of Several Inequalities Related to Multivariate Geometric Means

“…For more information on the Schur convexity and the Schur geometric convexity, please refer to the papers [23][24][25][26] and the monographs [20,22]. [27,28]).…”

“…For k = n, by Relations (10) and (11) and by Definitions 2 and 3, the inequalities in (25) and (26) hold. Theorem 3 is thus proven.…”

Some new integral inequalities of the Simpson type for MT-convex functions

“…Due to wide applications of various convex functions, some mathematicians have dedicated to studying integral inequalities of the HermiteHadamard type for dierent classes of convex functions. For details, please refer to [1,3,5,12,16,17,18,19,20,21,22,23] and closely related references therein.…”