Il'inskii, AOstrovska, SMathematics2024-07-052024-07-0520021270021-904510.1006/jath.2001.36572-s2.0-0036287075https://doi.org/10.1006/jath.2001.3657https://hdl.handle.net/20.500.14411/1114Let f is an element of C[0, 1], q is an element of (0, 1), and B-n(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 {B-n(f, q; x)}(n=1)(infinity). It is shown that in general these properties are essentially different from those in the classical case q = 1. (C) 2002 Elsevier Science (USA).eninfo:eu-repo/semantics/openAccessgeneralized Bernstein polynomialsq-integersq-binomial coefficientsconvergenceArticleQ21161100112WOS:000176197200005