Fejér–Hermite–Hadamard type inequalities involving generalized h -convexity on fractal sets and their applications

Chunyan Luo a, Hao Wang a, Tingsong Du a , b , ∗

Abstract: This article aims to investigate certain inequalities for generalized h -convexity on fractal sets R α , which are related to the famous Fejér–Hermite–Hadamard inequality. For this purpose, two identities for local differentiable mappings are established, based on which we provide certain estimates for the difference between the left and middle part as well as that of the middle and right part in the Fejér–Hermite–Hadamard inequality. Furthermore, we present five examples to illustrate the obtained results. As applications related to local fractional integrals, we construct several inequalities for random variables, cumulative distribution functions and numerical integrations.