New Generalized Class of Convex Functions and Some Related Integral Inequalities

Abstract

There is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the (n,m)–generalized convex and studied its basic algebraic properties. The Hermite–Hadamard inequality for the (n,m)–generalized convex function, for the products of two functions and of this type, were proven. Moreover, this class of functions was applied to several known identities; midpoint-type inequalities of Ostrowski and Simpson were derived. Our results are extensions of many previous contributions related to integral inequalities via different convexities.

Keywords

• Hermite–Hadamard inequality
• Ostrowski inequality
• Simpson inequality
• (<i>n</i>,<i>m</i>)–generalized convexity