Some New Jensen–Mercer Type Integral Inequalities via Fractional Operators

Abstract

In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.

Keywords

• convex functions
• (<i>h</i>,<i>m</i>)-convex functions
• Jensen–Mercer inequality
• Hermite–Hadamard inequality
• Hölder inequality
• power mean inequality