A new bound for the Jensen gap pertaining twice differentiable functions with applications

Abstract

In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory.

k -Fractional Variants of Hermite-Mercer-Type Inequalities via s -Convexity with Applications

“…for all ζ j ∈ ½ θ 1 , θ 2 , ρ j ∈ ½0, 1, and j = 1, 2, ⋯, n. It is one of the key inequalities that helps to extract bounds for useful distances in information theory (see [3,4]).…”

Uniform Treatment of Jensen’s Inequality by Montgomery Identity

“…Taking into consideration the tremendous applications of Jensen's inequality in various fields of mathematics and other applied sciences, the generalizations and improvements of Jensen's inequality have been a topic of supreme interest for the researchers during the last few decades as evident from a large number of publications on the topic (see [2][3][4] and the references therein). e well-known Jensen's inequality asserts that for the function Γ it holds that…”

n–polynomial exponential type p–convex function with some related inequalities and their applications

“…Eventually the theory of inequalities may be regarded as an independent area of mathematics. For the applications of inequalities interested readers refer to [1,2,3,4,5,6]. In recent years, a wide class of integral inequalities is being derived via different concepts of convexity.…”

“…It is also known as classical equation of (H-H) inequality. The Hermite-Hadamard inequality asserts that, if a function ∶ ⊂ ℜ → ℜ is convex in for 1 , 2 ∈ and 1 < 2 , then Interested readers can refer to [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”