New fractional inequalities of midpoint type via s-convexity and their application

Abstract

In this study, we introduced new integral inequalities of Hermite-Hadamard type via s-convexity and studied their properties. The absolute form of the first and second derivatives for the new inequalities is considered to be s-convex. As an application, the inequalities were applied to the special means of real numbers. We give the error estimates for the midpoint formula.

Some Integral Inequalities for <em>h</em>-Godunova-Levin Preinvexity

“…Usually, the preinvex functions can be convexity if ζ(u 2 , u 1 ) = u 2 − u 1 holds in (2). Other properties of preinvex functions are given in [15,16].…”

“…These inequalities have been extensively improved and generalized. For example, see [1,2,3,5] and [21].…”

New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

“…inequality for regular convex function was studied by [3]. Furthermore, many researchers have been studying the generalization of inequality in (1) motivated by various modifications of the notion of convexity, such as s-convexity and generalized s-convexity, for example see the details in ( [4][5][6][7]), where Hermite-Hadamard inequality were extended in order to include the problems that related to fractional calculus, a branch of calculus dealing with derivatives and integrals of non-integer order (see [8][9][10][11][12][13]). Nowadays, the real-life applications of fractional calculus exist in most areas of studies [14,15].…”

New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

“…This inequality is extended to include problems related to fractional calculus, a branch of calculus dealing with derivatives and integrals of non-integer order (see [9,3,20,5,16,10,15]). Nowadays, the real-life applications of fractional calculus exist in most areas of studies [1,2].…”