New discrete inequalities of Hermite–Hadamard type for convex functions

Abstract

Abstract We introduce new time scales on Z $\mathbb{Z}$ . Based on this, we investigate the discrete inequality of Hermite–Hadamard type for discrete convex functions. Finally, we improve our result to investigate the discrete fractional inequality of Hermite–Hadamard type for the discrete convex functions involving the left nabla and right delta fractional sums.

Keywords

• Time scale
• Hermite–Hadamard inequality
• Convex functions