On generalized Bernstein Kantorovich Schurer type operators and its approximation behaviour

Abstract

In the present paper, we introduce generalized Bernstein Kantorovich Schurer type operators and its approximation properties. Firstly, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections. In continuation, local and global approximation properties are studied in terms of first and second order modulus of smoothness, Peetre’s K-functional and weight functions in various functional spaces.