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Generalized Hermite-Hadamard Inequalities on Discrete Time Scales

This paper is concerned with some new Hermite-Hadamard inequalities on two types of time scales, Z and Nc,h. Based on the substitution rules, we first prove the discrete Hermite-Hadamard inequalities on Z relating to the midpoint a+b2 and extend them to discrete fractional forms. In addition, by using traditional methods, we prove discrete Hermite-Hadamard inequalities on Nc,h and explore the corresponding fractional inequalities involving the nabla h-fractional sums. Finally, two examples are given to illustrate the obtained results.