In this study, we introduce a new conformable derivative, namely the beta-conformable derivative. We derive Taylor?s theorem for also investigate some properties of and useful related theorems light operator, extend recent classical integral inequalities including Steffensen Hermite-Hadamard inequality.

Abstract Local fractional integral inequalities of Hermite-Hadamard type involving local operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities. In this article, we analyze Hermite-Hadamard-type via ( h <m:mo...

The purpose of this paper is to study a generalization strongly $\eta$-convex functions using the fractal calculus developed by Yang \cite{Yang}, namely generalized function. Among other results, we obtain some Hermite-Hadamard and Fej\'er type inequalities for class functions.

Given a function f : I → J and a pair of means M and N, on the intervals I and J respectively, we say that f is MN -convex provided that f (M(x, y)) N(f (x), f (y)) for every x , y ∈ I . In this context, we prove the validity of all basic inequalities in Convex Function Theory, such as Jensen’s Inequality and the Hermite-Hadamard Inequality. Mathematics subject classification (2000): 26A51, 26D...