Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series

U. Goginava; K. Nagy

doi:10.1007/s10476-016-0203-0

Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series

U. Goginava, K. Nagy

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

2 Citations (Scopus)

Abstract

In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.

Original language	English
Pages (from-to)	143-157
Number of pages	15
Journal	Analysis Mathematica
Volume	42
Issue number	2
DOIs	https://doi.org/10.1007/s10476-016-0203-0
Publication status	Published - Jun 1 2016
Externally published	Yes

Keywords

Marcinkiewicz mean
strong approximation
Walsh–Kaczmarz function

ASJC Scopus subject areas

Analysis
General Mathematics

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10.1007/s10476-016-0203-0

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abstract = "In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.",

keywords = "Marcinkiewicz mean, strong approximation, Walsh–Kaczmarz function",

author = "U. Goginava and K. Nagy",

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T1 - Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series

AU - Goginava, U.

AU - Nagy, K.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.

AB - In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.

KW - Marcinkiewicz mean

KW - strong approximation

KW - Walsh–Kaczmarz function

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JF - Analysis Mathematica

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ER -

Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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