Abstract
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.
Funder
National Science Foundation of China
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Reference25 articles.
1. Convex Functions, Partial Orderings, and Statistical Applications;Pečarić,1992
2. Convex Functions on Discrete Time Domains
3. Selected Topics on Hermite-Hadamard Inequalities and Applications;Dragomir,2000
4. Advances in Mathematical Inequalities and Applications;Agarwal,2018
5. Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities