Lupas-Kantorovich Type Operators for Functions of Two Variables

Agratini [1] introduced the Lupas-Kantorovich type operators. Manav and Ispir [18] defined a Durrmeyer variant of the operators proposed by Lupas and studied some of their approximation properties. Later, they [17] considered the bivariate case of these operators and studied the degree of approximation by means of the complete and partial moduli of continuity and the order of convergence by using Peetre's K-functional. The associated GBS (Generalized Boolean Sum) operators were also investigated in the same paper. Our goal is to define the bivariate Chlodowsky Lupas-Kantorovich type operators and study their degree of approximation. We also introduce the associated GBS operators and investigate the rate of convergence of these operators for Bogel continuous and Bogel differentiable functions with the aid of mixed modulus of smoothness.