On Ostrowski–Mercer’s Type Fractional Inequalities for Convex Functions and Applications

Abstract

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed of convex functions and their properties. The results were directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma functions and modified Bessel functions, some applications of the acquired results were obtained.

Keywords

• convex function
• Ostrowski’s inequality
• Mercer inequality
• Riemann–Liouville fractional integral operators
• special means
• <i>q</i>-digamma functions