Inequalities via s−convexity and log −convexity

Abstract

Abstract:In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s−convex and log −convex. Also, we give some applications for numerical integration.

The most important inequalities of $m$-convex functions

“…We begin the section by recalling the important Fejér inequality (see [3]) and the famous Hermite-Hadamard inequality (see [4,5] 1) and the substitution h(x) = 1 yields the Hermite-Hadamard inequality:…”

“…Inequalities for m-convex functions on the bounded interval of nonnegative real numbers were considered in [2]. Research on inequalities via s-convexity and log -convexity can be found in [1]. Usage of functionals in studying inequalities can be seen in [13].…”