Approximation Theorems for Functions of Two Variables via σ-Convergence

Approximation Theorems for Functions of Two Variables via σ-Convergence

Çakan et al. (2006) introduced the concept of σ-convergence for double sequences. In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, and x2+y2 and construct an example by considering the Bernstein poly...

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Main Author: Mohammed A. Alghamdi
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2014/350474
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spelling doaj-e8492a72a85f44b1978fe05e4c1de8a22020-11-24T22:27:41ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/350474350474Approximation Theorems for Functions of Two Variables via σ-ConvergenceMohammed A. Alghamdi0Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaÇakan et al. (2006) introduced the concept of σ-convergence for double sequences. In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, and x2+y2 and construct an example by considering the Bernstein polynomials of two variables in support of our main result.http://dx.doi.org/10.1155/2014/350474
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed A. Alghamdi
spellingShingle Mohammed A. Alghamdi
Approximation Theorems for Functions of Two Variables via σ-Convergence
Journal of Function Spaces
author_facet Mohammed A. Alghamdi
author_sort Mohammed A. Alghamdi
title Approximation Theorems for Functions of Two Variables via σ-Convergence
title_short Approximation Theorems for Functions of Two Variables via σ-Convergence
title_full Approximation Theorems for Functions of Two Variables via σ-Convergence
title_fullStr Approximation Theorems for Functions of Two Variables via σ-Convergence
title_full_unstemmed Approximation Theorems for Functions of Two Variables via σ-Convergence
title_sort approximation theorems for functions of two variables via σ-convergence
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2014-01-01
description Çakan et al. (2006) introduced the concept of σ-convergence for double sequences. In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, and x2+y2 and construct an example by considering the Bernstein polynomials of two variables in support of our main result.
url http://dx.doi.org/10.1155/2014/350474
work_keys_str_mv AT mohammedaalghamdi approximationtheoremsforfunctionsoftwovariablesviasconvergence
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