Hermite-Hadamard-Mercer Type Inequalities for Twice Differentiable Convex Involving Riemann-Liouville Fractional Integrals

Abstract

In this study, authors use Riemann-Liouville fractional integrals to get several new inequalities of Hermite-Hadamard-Mercer type. We establish some trapezoid and midpoint type inequalities for functions whose twice derivatives in absolute value are convex involving Riemann-Liouville fractional integrals. The results of the paper are extensions and refinements of Hermite-Hadamard and Hermite-Hadamard-Mercer type inequalities. we discuss special cases of our main results and give new inequalities of the Hermite-Hadamard and Hermite-Hadamard-Mercer type. These results are accompanied by further remarks and observations. Next, we see the efficiency of our inequalities via some applications on special means. Lastly, a couple of examples through graphical visualizations are provided to illustrate the key findings of our research.