Convergence of generalized Bernstein polynomials

Abstract

Let f ε C[0, 1], q ε (0, 1), and Bn (f, q; x) be generalized Bernstein polynomials based on the q-integers. These polynomials were introduced by G. M. Phillips in 1997. We study convergence properties of the sequence {Bn(f, q; x)}n=1∞. It is shown that in general these properties are essentially different from those in the classical case q = 1. © 2002 Elsevier Science (USA).