Inequalities for Riemann–Liouville Fractional Integrals of Strongly $\left(s,m\right)$-Convex Functions

Abstract

The results of this paper provide two Hadamard-type inequalities for strongly s , m -convex functions via Riemann–Liouville fractional integrals and error estimations of well-known fractional Hadamard inequalities. Their special cases are given and connected with the results of some published papers.

Hermite-Hadamard type inequalities for Riemann-Liouville Fractional Integrals via strongly h-convex functions

“…In 2020, the authors [6] extended them to more generalized fractional integrals. In 2021, the authors [46] gained similar inequalities for strongly (s, m)−convex functions. On the other hand, Noor and Awan [23] proved an equality for twice differentiable functions.…”

“…In 2020, Budak, Ertugral and Sarikaya [6] extended it to more generalized fractional integrals. In 2021, Zhang, Farid and Akbar [46] obtained an analogue inequality as Theorem B for strongly (s, m)−convex functions. In this section, we establish the following similar inequality for strongly h−convex functions.…”

“…If taking h(t) = t and h(t) = t s , then Theorem 1 reduces to Corollary 3 and Corollary 4 in [46], respectively. And, it is not difficult to see that the theorem is Theorem A for α = 1.…”