Some generalized Hermite-Hadamard type integral inequalities for generalized s-convex functions on fractal sets

Abstract

In this article, some new integral inequalities of generalized Hermite-Hadamard type for generalized s-convex functions in the second sense on fractal sets have been established. MSC:26A51; 26D07; 26D15; 53C22

Certain integral inequalities related to $(\varphi,\varrho^{\alpha})$-Lipschitzian mappings and generalized h-convexity on fractal sets

“…Furthermore, we discovered certain properties of generalized mappings H and generalized mappings F associated with generalized h-convexity mappings. The results proved in this paper generalize the corresponding results presented by Ahmad, Jleli and Samet [7] and Kiliçman and Saleh [12].…”

“…Moreover, we give some properties of generalized mappings H and F, which are naturally related to the generalized h-convex functions. The results present in this paper extend the results obtained by Ahmad, Jleli and Samet [7] and Kiliçman and Saleh [12].…”

“…For example, Mo, Sui and Yu [11] established the generalized Jensen's inequality and generalized Hermite-Hadamard's inequality for generalized convex mappings. Kiliçman and Saleh [12,13] studied generalized Hadamard's type inequalities for generalized s-convex mappings. Erden and Sarikaya [14] gave some generalized Pompeiu's type inequalities associating with local fractional integrals.…”

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].…”

On some inequalities for generalized s-convex functions and applications on fractal sets

“…for s ∈ (0, 1), then it is the best possible in the second inequality (1.4), the proof was started by Kiliçman and Saleh [10]. There are many researchers studied the properties of functions on fractal space and constructed many kinds of fractional calculus by using different approaches; see [3,18,21].…”