Convergence of generalized Bernstein polynomials

被引：133

作者：

Il'inskii, A

Ostrovska, S

机构：

[1] Kharkov Natl Univ, Dept Math & Mech, UA-61077 Kharkov, Ukraine

[2] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey

来源：

JOURNAL OF APPROXIMATION THEORY | 2002年 / 116卷 / 01期

关键词：

generalized Bernstein polynomials; q-integers; q-binomial coefficients; convergence;

D O I：

10.1006/jath.2001.3657

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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).

引用

页码：100 / 112

页数：13

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