Weighted approximation and GBS of Chlodowsky–Szász–Kantorovich type operators

Abstract

The present paper deals with the approximation properties of the bivariate operators which are the combination of Bernstein–Chlodowsky operators and the Szasz–Kantorovich type operators. We investigate the degree of approximation of the bivariate operators for continuous functions in the weighted space of polynomial growth. Further, we introduce the Generalized Boolean Sum (GBS) of these bivariate Chlodowsky–Szasz–Kantorovich type operators and examine the order of approximation in the Bogel space of continuous functions by means of the Lipschitz class and mixed modulus of smoothness. Besides this, we compare the rate of convergence of the Chlodowsky–Szasz–Kantorovich type operators and the associated GBS operators by numerical examples and tables using Maple algorithms. It turns out that the GBS operator converges faster to the function than the original operator.