Hermite-Hadamard Inequalities for Generalized (m - F)-Convex Function in the Framework of Local Fractional Integrals.

This work presents new versions of the Hermite-Hadamard Inequality, for (m-F)-convex functions, defined on fractal sets R ς (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 Hölder-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. 2020 Mathematics Subject Classification. [ABSTRACT FROM AUTHOR]