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.