Refined Bounds of the Quantum QuadraturesWithin the Class of Distance-Disturbed Convex Functions in Two Dimensions

Abstract

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 proper-
ties. 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.