Abstract
Preliminaries of q-calculus for functions of two variables over finite rectangles in the plane are introduced. Some q-analogues of the famous Hermite–Hadamard inequality of functions of two variables defined on finite rectangles in the plane are presented. A q1q2-Hölder inequality for functions of two variables over finite rectangles is also established to provide some quantum estimates of trapezoidal type inequality of functions of two variables whose q1q2-partial derivatives in absolute value with certain powers satisfy the criteria of convexity on co-ordinates.