Abstract
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
) 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.