New versions of Hermite–Hadamard inequalities on Discrete Time Scales

Abstract

In this paper, we first introduced two time scales based on the interval [a, b] and \( \mathbb {Z} \). Then, by using one of these time scale and substitutions rules, we prove a new version of discrete Hermite-Hadamard inequality for discrete convex functions. Moreover, we investigate the fractional version of this inequality involving fractional delta and nabla sums.