New Generalized Class of Convex Functions and Some Related Integral Inequalities.

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. [ABSTRACT FROM AUTHOR]