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.

New Estimates on Hermite–Hadamard Type Inequalities via Generalized Tempered Fractional Integrals for Convex Functions with Applications

“…Over the years, researchers have made significant contributions to the development and generalization of the H-H inequality. These efforts have led to the exploration of various generalizations, extensions, and refinements of the original inequality, involving different types of functions, operators, and integral formulations; for example, Bayraktar et al [2] proved Mercer versions, Sahoo et al [3] established H-H inequalities via Atangana-Baleanu fractional operators, Tariq et al [4] presented Simpson-Merer-type inequalities with the help of Atangana-Baleanu fractional operators, and for new versions of H-H results involving exponential kernels, one can refer to [5] and Bayraktar et al [6], who employed a modified (h,m,s) convex function to establish weighted H-H inequalities. These advancements have broadened the scope of the H-H inequality and deepened our understanding of convex functions.…”