On the approximation properties of Cesàro means of negative order of Walsh-Fourier series

Ushangi Goginava

doi:10.1006/jath.2001.3632

On the approximation properties of Cesàro means of negative order of Walsh-Fourier series

Ushangi Goginava

Research output: Contribution to journal › Article › peer-review

49 Citations (Scopus)

Abstract

In this paper we establish approximation properties of Cesàro (C, -α)-means with α ε (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ^-α_n (f, x) to f (x) in the L^p-metric. We also show that this condition cannot be improved in the case p = 1.

Original language	English
Pages (from-to)	9-20
Number of pages	12
Journal	Journal of Approximation Theory
Volume	115
Issue number	1
DOIs	https://doi.org/10.1006/jath.2001.3632
Publication status	Published - 2002
Externally published	Yes

Keywords

Approximation
Cesàro means
Walsh functions

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1006/jath.2001.3632

Cite this

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abstract = "In this paper we establish approximation properties of Ces{\`a}ro (C, -α)-means with α ε (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ-αn (f, x) to f (x) in the Lp-metric. We also show that this condition cannot be improved in the case p = 1.",

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AB - In this paper we establish approximation properties of Cesàro (C, -α)-means with α ε (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ-αn (f, x) to f (x) in the Lp-metric. We also show that this condition cannot be improved in the case p = 1.

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KW - Cesàro means

KW - Walsh functions

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On the approximation properties of Cesàro means of negative order of Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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