Some new Hermite–Hadamard type inequalities for s-convex functions and their applications

Abstract

In this paper, we establish some new integral inequalities of Hermite-Hadamard type for s-convex functions by using the Hölder-İşcan integral inequality. We also compare our new results with the known results and show that the results which we obtained are better than the known results. Finally, we give some applications to trapezoidal formula and to special means. MSC: 26D15; 26A51

Exponential type convexity and some related inequalities

“…Convexity theory provides powerful principles and techniques for studying a class of problems in mathematics. See articles [4,5,7,[9][10][11][12][13] and the references therein. Let f : I → R be a convex function.…”

Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

“…Following this, many important generalizations of Hermite-Hadamard inequality were studied [9,10,11,12,13,14], some of which were formulated via generalized s-convexity, which is defined as follows.…”

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].…”