Notions of generalized s-convex functions on fractal sets

Abstract

The purpose of this article is to present some new inequalities for products of generalized convex and generalized s-convex functions on fractal sets. Furthermore, some applications are given.MSC: 26A51; 26D07; 26D15; 53C22

New Hermite-Hadamard and Jensen Type Inequalities for h-Convex Functions on Fractal Sets

“…In this article motivated and inspired by the ongoing research in the field [13,14,21,22],we establish new Hermite-Hadamard and Jensen type inequalities for h-convex functions on fractal sets.…”

Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property

“…Local fractional inequalities and their fertile applications in pure and applied mathematics have attracted the attention of many researchers [15,16]. For example, Mo et al [17] derived the generalized Hermite-Hadamard inequality for generalized convex functions.…”

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

“…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.…”