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Refined bounds of the quantum quadratures within the class of distance-disturbed convex functions in two dimensions

In this paper, we introduce the class of disturbed convex functions defined
 by means of distance perturbations in two dimensions on co-ordinates. Some
 quantum trapezoidal estimations are obtained for functions having two
 dimensional distance-disturbed convexity properties. Refined bounds of the
 quantum integrals of distance-disturbed convex functions on coordinates are
 deduced by using the rectangular finite elements technique. These
 approximations are as best as possible from the sharpness point of view. The
 sharpness of few results from the literature follows as consequence of the
 new results in this paper.