On Some New Ostrowski–Mercer-Type Inequalities for Differentiable Functions

Abstract

In this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski–Mercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of the Ostrowski inequalities established inside the literature. There are also some applications to the special means of real numbers given.

Keywords

• Ostrowski inequality
• Jensen–Mercer inequality
• convex functions