The Bézier variant of Lupas Kantorovich operators based on Polya distribution

摘要

In this paper we introduce the B′ ezier variant of Lupas Kantorovich operators based on Polya distribution. We establish a direct approximation by means of the Ditzian-Totik mod- ulus of smoothness and a global approximation theorem in terms of second order modulus of continuity. Furthermore, we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded function. Our results extend the work of Agrawal [P. N. Agrawal, N. Ispir and A. Kajla, Approximation properties of Lupas-Kantorovich operators based on polya distribution, Rendiconti del Circolo Matematico di Palermo Series 2, 2016, 65 (2): 185–208] and Ispir [N. Ispir, P. N. Agrawal and A. Kajla, Rate of convergence of Lupas Kantorovich operators based on Polya distribution, Appl. Math. Comput., 2015, 261: 323–329].