Certain midpoint-type Fejér and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel

Abstract

<abstract><p>In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejér type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.</p></abstract>

On Further Inequalities for Convex Functions via Generalized Weighted-Type Fractional Operators

“…Convex analysis has become one of the important application areas of fractional analysis (see [1][2][3][4][5][6][7][8][9]). In addition, several mathematicians have studied certain inequalities for convex functions using different types of integral operators (for example, the R-L fractional integral operator, the conformable fractional integral operator, tempered fractional integral operators, generalized proportional integral operators, and generalized proportional Hadamard integral operators).…”