Some Inequalities Using Generalized Convex Functions in Quantum Analysis

Abstract

In the present work the Hermite-Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in (0, 1] and two arbitrary real functions defined on [0, 1]. From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions. Also, the definition of dominated convex functions respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established.