On the uniform strong approximation of Marcinkiewicz type for multivariable continuous functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the uniform strong approximation of Marcinkiewicz type for multivariable continuous functions

Authors:

Institution:

(1) Department of Mathematics, Hebei North University, 075027 Zhangjiakou, P. R. China;(2) Beijing 101 Secondary School, 100091 Beijing, P. R. China

Abstract:

The rate of uniform strong approximation of Marcinkiewicz type for multivariable continuous functions is obtained in this paper as follows:

$\parallel \frac{1}{{k + 1}}\sum\limits_{j = 0}^k {|S_j (f) - f|^q } \parallel \leqslant \frac{C}{{k + 1}}\sum\limits_{j = 0}^k {E_j^q (f),}$

where S_j(f) denotes the square partial Fourier sum of f and E_j(f) denotes the square best approximation of f by trigonometric polynomials of degree (j,j,…,j), j=0,1,2,… Supported by NSF of China, under the Grant 10471010.

Keywords:

square partial Fourier sum strong approximation of Marcinkiewiecz type FUNCTIONS CONTINUOUS MULTIVARIABLE TYPE square partial Fourier sum best approximation polynomials degree rate strong approximation type multivariable continuous paper

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