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-alpha (0 < alpha <= 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 Fejer-Hermite-Hadamard (Fejer-H-H) types inequalities. We also obtained a new result of the Fejer-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, numerical integrations and generalized to special means. (C) 2021 Elsevier Ltd. All rights reserved.