Degree of approximation for bivariate extension of Chlodowsky-type q-Bernstein–Stancu–Kantorovich operators

摘要

In this paper, we introduce the bivariate generalization of the Chlodowsky-type q-Bernstein–Stancu–Kantorovich operators on an unbounded domain and studied the rate of convergence in terms of the Lipschitz class function and complete modulus of continuity. Further, we establish the weighted approximation properties for these operators. The aim of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetre’s K- functional. Then, we give generalization of the operators and investigate their approximations. Furthermore, we show the convergence of the bivariate Chlodowsky-type operators to certain functions by illustrative graphics using Python programming language. Finally, we construct the GBS operators of bivariate Chlodowsky-type q-Bernstein–Stancu–Kantorovich and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.