Rate of Convergence of parametrically generalized bivariate Baskakov-Stancu operators

Abstract

In the present work, we consider Stancu variant of a bivariate parametrically generalised Baskakov operator. We discuss the rate of convergence of these operators by means of partial moduli of continuity and modulus of continuity of second order. Also, we prove Vornovskaja type assymptotic theorem. Furthermore, the Generalized Boolean Sum (GBS) operators associated to Stancu variant of a-Baskakov operators are constructed and we study their order of convergence using mixed modulus of smoothness for B$\ddot{o}$gel continuous and B$\ddot{o}$gel differentiable functions. Some surface plotting illustrating the approximation for different values of Stancu variables and the error of approximation by the proposed operators are also given using MATLAB programming.