On the q-Bernstein polynomials of piecewise linear functions in the case q > 1

被引：2

作者：

Kaskaloglu, Kerem ^{[1
]}

Ostrovska, Sofiya ^{[1
]}

机构：

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

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2013年 / 57卷 / 9-10期

关键词：

q-integers; q-binomial coefficients; q-Bernstein polynomials; q-Bernstein operator; Operator norm; CONVERGENCE; APPROXIMATION; SATURATION; OPERATORS;

D O I：

10.1016/j.mcm.2012.01.022

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The aim of this paper is to present new results related to the approximation of continuous functions by their q-Bernstein polynomials in the case q > 1. The first part of the paper is devoted to the behavior of the q-Bernstein polynomials of piecewise linear functions. This study naturally leads to the notion of truncated q-Bernstein polynomials introduced in the paper. The second part deals with the asymptotic estimates for the norms of the m-truncated q-Bernstein polynomials, in the case where both n and q vary. The results of the paper are illustrated by numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：2419 / 2431

页数：13

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On the q-Bernstein polynomials of piecewise linear functions in the case q &gt; 1

On the q-Bernstein polynomials of piecewise linear functions in the case q > 1