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 sets ${\mathbb{R}}^{\alpha }$ $(0<\alpha \le 1)$. 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. Some applications to random variables and numerical integrations are studied.

15 pages

References in corpus (1)

• On (h-m)-Convexity and Hadamard-Type Inequalities

Cited by in corpus (1)

• A Systematic Review on Hermite-Hadamard Inequality: Theory and Applications