Some Hermite–Hadamard and Opial dynamic inequalities on time scales

Abstract

Abstract In this article, we are interested in some well-known dynamic inequalities on time scales. For this reason, we will prove some new Hermite–Hadamard (H-H) and Opial dynamic inequalities on time scales. The main results here will be derived via the dynamic integration by parts and chain rule formulas on time scales. In addition, we will extend and unify the inequalities for the convex functions.

Keywords

• Time scales
• H-H inequality
• Steffensen inequalities
• Opial inequality
• Hölder’s inequality