Convergence of generalized Bernstein polynomials

JOURNAL OF APPROXIMATION THEORY

卷:116

Article

Il'inskii, A ; Ostrovska, S

关键词: generalized Bernstein polynomials;    q-integers;    q-binomial coefficients;    convergence;   

DOI  :  10.1006/jath.2001.3657

来源: Elsevier

【 摘 要 】

Let 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).

【 授权许可】

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