Some Inequalities of Hermite–Hadamard Type for MT-h-Convex Functions via Classical and Generalized Fractional Integrals. (16th July 2022) - Qi, Hengxiao; Nazeer, Waqas; Abbas, Fatima; Liao, Wenbo
Abstract : Convexity plays a vital role in pure and applied mathematics specially in optimization theory, but the classical convexity is not enough to fulfil the needs of modern mathematics; hence, it is important to study generalized notion of convexity. Fraction integral operators also become an important tool for solving problems of model physical and engineering processes that are found to be best described by fractional differential equations. The aim of this paper is to study MT-h-convex functions via fractional integral operators. We establish several Hermite–Hadamard-type inequalities for MT-h-convex function via classical and generalized fractional integrals. We also obtain special means related to our results and present some error estimates for the trapezoidal formulas.