On the rate of convergence of Baskakov-Kantorovich-Bezier operators for bounded variation functions (original) (raw)

On the rate of convergence of some operators on functions of bounded variation

Journal of Approximation Theory, 1989

Let L,(f; x) denote the Feller operator where f is a function of bounded variation. The rates of convergence are determined by estimating IL,(J x)-f(x)1 in terms of certain bounds. These results extend and sharpen the results of Cheng [J. Approx. Theory 39 (1983), 259-2741 for Bernstein polynomials. Several classical operators are discussed as examples.

Bèzier variant of the generalized Baskakov Kantorovich operators

Bollettino Dell'unione Matematica Italiana, 2015

In this paper, we introduce the Bèzier variant of the generalized Baskakov Kantorovich operators. We establish a direct approximation theorem with the aid of the Ditzian-Totik modulus of smoothness and also study the rate of convergence for the functions having a derivative of bounded variation for these operators.