Approximation by bivariate generalized sampling series in weighted spaces of functions

In this paper, we study weighted approximation by bivariate generalized sampling series. Considering polynomially weighted spaces of bivariate functions we obtain pointwise and uniform convergence of the series. A rate of convergence is also presented by means of weighted modulus of continuity. In order to determine a rate of pointwise convergence, after estimating remainder of Taylor expansion of bivariate function with weighted modulus of continuity, we present a quantitative Voronovskaja theorem. Some numerical examples are also given.