Jensen-Mercer Type Inequalities in the Setting of Fractional Calculus with Applications

Abstract

The main objective of this paper is to establish some new variants of the Jensen–Mercer inequality via harmonically strongly convex function. We also propose some new fractional analogues of Hermite–Hadamard–Jensen–Mercer-like inequalities using AB fractional integrals. In order to obtain some of our main results, we also derive new fractional integral identities. To demonstrate the significance of our main results, we present some interesting applications to special means and to error bounds as well.

Keywords

• Hermite–Hadamard–Mercer inequality
• Hölder’s inequality
• Riemann–Liouville fractional integrals
• harmonic convex function
• special means
• error estimation