The saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials in the case q > 1

Zhuangzhi Wu

doi:10.1016/j.jmaa.2009.04.003

The saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials in the case q > 1

Zhuangzhi Wu^*

^*此作品的通讯作者

计算机学院

科研成果: 期刊稿件 › 文章 › 同行评审

19 引用（Scopus）

摘要

In the note, we consider saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials of a continuous function f for arbitrary fixed q > 1. We show that the rate of uniform convergence on [0, 1] is o (q^{- n}) if and only if f is linear. The result is sharp in the following sense: it ceases to be true if we replace "o" by "O".

源语言	英语
页（从-至）	137-141
页数	5
期刊	Journal of Mathematical Analysis and Applications
卷	357
期	1
DOI	https://doi.org/10.1016/j.jmaa.2009.04.003
出版状态	已出版 - 1 9月 2009

访问文件

10.1016/j.jmaa.2009.04.003

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{8f661598d6194121b506be5434595872,

title = "The saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials in the case q > 1",

abstract = "In the note, we consider saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials of a continuous function f for arbitrary fixed q > 1. We show that the rate of uniform convergence on [0, 1] is o (q- n) if and only if f is linear. The result is sharp in the following sense: it ceases to be true if we replace {"}o{"} by {"}O{"}.",

keywords = "Saturation, q-Bernstein polynomials",

author = "Zhuangzhi Wu",

year = "2009",

month = sep,

day = "1",

doi = "10.1016/j.jmaa.2009.04.003",

language = "英语",

volume = "357",

pages = "137--141",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - The saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials in the case q > 1

AU - Wu, Zhuangzhi

PY - 2009/9/1

Y1 - 2009/9/1

N2 - In the note, we consider saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials of a continuous function f for arbitrary fixed q > 1. We show that the rate of uniform convergence on [0, 1] is o (q- n) if and only if f is linear. The result is sharp in the following sense: it ceases to be true if we replace "o" by "O".

AB - In the note, we consider saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials of a continuous function f for arbitrary fixed q > 1. We show that the rate of uniform convergence on [0, 1] is o (q- n) if and only if f is linear. The result is sharp in the following sense: it ceases to be true if we replace "o" by "O".

KW - Saturation

KW - q-Bernstein polynomials

UR - https://www.scopus.com/pages/publications/67349288122

U2 - 10.1016/j.jmaa.2009.04.003

DO - 10.1016/j.jmaa.2009.04.003

M3 - 文章

AN - SCOPUS:67349288122

SN - 0022-247X

VL - 357

SP - 137

EP - 141

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

The saturation of convergence on the interval [0, 1] for the q-Bernstein polynomials in the case q > 1

摘要

访问文件

其它文件与链接

指纹

引用此