Generalized Fejér-Hermite-Hadamard type via generalized $(h-m)$-convexity on fractal sets and applications

Abstract

In this article, we define a new class of convexity called generalized (h − m)-convexity, which generalizes h-convexity and m-convexity on fractal set R α (0 < α ≤ 1). Some properties of this new class are discussed. Using local fractional integrals and generalized (h − m)-convexity, we generalized Hermite-Hadamard (H-H) and Fejér-Hermite-Hadamard (Fejér-H-H) types inequalities. We also obtained a new result of the Fejér-H-H type for the function whose derivative in absolute value is the generalized (h − m)-convexity on fractal sets. As applications, we studied some new inequalities for random variables and numerical integrations.