Approximation of BB-continuous and BB-differentiable functions by GBS operators of qq-Bernstein-Schurer-Stancu type

Abstract

Bˇarbosu and Muraru (2015) introduced the bivariate generalization of the q -Bernstein Schurer Stancu operators and constructed a GBS operator of q -Bernstein Schurer Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In the last section we estimate the degree of approximation by means of Lipschitz class function and the rate of convergence with the help of mixed modulus of smoothness for the GBS operator of q -Bernstein Schurer Stancu type. Furthermore, we show comparisons by some illustrative graphics in Maple for the convergence of the operators to some functions.