Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals

Abstract

The aim of this paper is to establish Hermite-Hadamard, Hermite-Hadamard-Fejér, Dragomir-Agarwal and Pachpatte type inequalities for new fractional integral operators with exponential kernel. These results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions. Furthermore, the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields.2000 Mathematics Subject Classification. 26A33; 26D10.

Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

“…As a result, some new integral inequalities by the approach of fractional calculus have been obtained in the literature until now. In addition, Ahmad et al [16] gave the new fractional integral operators with an exponential kernel and proved similar inequalities.…”

“…Lemma 3 (see [16], Theorem 1). Let h : [a, b] → be a positive convex function with 0 ≤ a < b and h ∈ L[a, b].…”

“…Many extensive investigations have been carried out in this area. Due to the wide applications of Hermite-Hadamard inequalities and fractional integrals, many researchers have extended their research to Hermite-Hadamard inequalities involving fractional integrals rather than integer integrals, see [12][13][14][15][16][17][18][19][20][21][22]. Sarikaya et al [12] have deduced an amusing inequality of Hermite-Hadamard-type involving fractional integrals in the place of ordinary integrals.…”

“…In addition, Ahmad et al [16] derived the bound estimate of the difference between the mean value of the endpoints and the average of the fractional integrals.…”

“…Motivated by [12,15,16], we will demonstrate three new fractional-type integral identities and set up their corresponding Hermite-Hadamard-type inequalities involving left-sided and right-sided fractional integrals for convex functions, respectively.…”