Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane

By Muhammad Amer Latif, Sever Silvestru Dragomir, Ebrahim Momoniat. 2017

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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 q 1 q 2 -Holder 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 q 1 q 2 -partial derivatives in absolute value with certain powers satisfy the criteria of convexity on co-ordinates.

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