Generalization of some fractional versions of Hadamard inequalities via exponentially (α, <i>h</i> - <i>m</i>)-convex functions

Abstract

In this paper we give Hadamard inequalities for exponentially (alpha, h - m)-convex functions using Riemann-Liouville fractional integrals for strictly increasing function. Results for RiemannLiouville fractional integrals of convex, m-convex, s-convex, (alpha, m)-convex, (s, m)-convex, (h - m) convex, (alpha, h - m)-convex, exponentially convex, exponentially m-convex, exponentially s-convex, exponentially (s, m)-convex, exponentially (h - m)-convex, exponentially (alpha, h - m)-convex functions are particular cases of the results of this paper. The error estimations of these inequalities by using two fractional integral identities are also given.