k -Fractional Variants of Hermite-Mercer-Type Inequalities via s -Convexity with Applications

Abstract

This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville $k$ -fractional integral operators by employing $s$ -convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping $\Psi$ whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for ${\Psi }^{\prime }$ , ${\Psi }^{\prime \prime }$ , and ${\Psi }^{\prime \prime \prime }$ and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.