Hermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus

At first, we recall the q-operators in the context of q-calculus and by examining these operators we will introduce new definitions of the partial q-operators. Then, we investigate some new refinements inequalities of Hermite–Hadamard ( $H-H$ H − H ) type on the coordinated convex functions involving the new defined partial q-operators. From our main results, we establish several specific inequalities and we point out the existing results which had already been obtained in the literature.