Hermite-Hadamard inequalities for generalized (m-F)-convex function in the framework of local fractional integrals

Abstract

This work presents new versions of the Hermite-Hadamard Inequality, for (m−F)-convex functions, defined on fractal sets Rς ( 0 ς ≤ 1). So, we show some new results for twice differentiable functions using local fractional calculus, as well as some new definitions. We will construct these new integral inequality using the generalized H¨older-integral inequality and the power mean integral inequality. Furthermore, we present some new inequalities for the midpoint and trapezoid formulas in a novel type of fractal calculus. The conclusions in this paper are substantial advancements and generalizations of prior research reported in the literature.