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Korovkin second theorem via B-statistical A-summability

Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln) n ≥ 1 of positive linear operators on C [ 0,1 ] of all continuous functions on the real interval [ 0,1 ] is an approximation process. That is, these theorems exhibit a variety of test functions which assure...

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Main Authors: Mursaleen, Mohammad, Kilicman, Adem
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30126/1/30126.pdf
http://psasir.upm.edu.my/id/eprint/30126/
http://www.hindawi.com/journals/aaa/2013/598963/
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spelling my.upm.eprints.301262017-10-20T04:19:10Z http://psasir.upm.edu.my/id/eprint/30126/ Korovkin second theorem via B-statistical A-summability Mursaleen, Mohammad Kilicman, Adem Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln) n ≥ 1 of positive linear operators on C [ 0,1 ] of all continuous functions on the real interval [ 0,1 ] is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, x, and x 2 in the space C [ 0,1 ] as well as for the functions 1, cos, and sin in the space of all continuous 2 π -periodic functions on the real line. In this paper, we use the notion of B -statistical A -summability to prove the Korovkin second approximation theorem. We also study the rate of B -statistical A -summability of a sequence of positive linear operators defined from C 2 π (ℝ) into C 2 π (ℝ). Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30126/1/30126.pdf Mursaleen, Mohammad and Kilicman, Adem (2013) Korovkin second theorem via B-statistical A-summability. Abstract and Applied Analysis, 2013. art. no. 598963. pp. 1-6. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2013/598963/ 10.1155/2013/598963
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln) n ≥ 1 of positive linear operators on C [ 0,1 ] of all continuous functions on the real interval [ 0,1 ] is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, x, and x 2 in the space C [ 0,1 ] as well as for the functions 1, cos, and sin in the space of all continuous 2 π -periodic functions on the real line. In this paper, we use the notion of B -statistical A -summability to prove the Korovkin second approximation theorem. We also study the rate of B -statistical A -summability of a sequence of positive linear operators defined from C 2 π (ℝ) into C 2 π (ℝ).
format Article
author Mursaleen, Mohammad
Kilicman, Adem
spellingShingle Mursaleen, Mohammad
Kilicman, Adem
Korovkin second theorem via B-statistical A-summability
author_facet Mursaleen, Mohammad
Kilicman, Adem
author_sort Mursaleen, Mohammad
title Korovkin second theorem via B-statistical A-summability
title_short Korovkin second theorem via B-statistical A-summability
title_full Korovkin second theorem via B-statistical A-summability
title_fullStr Korovkin second theorem via B-statistical A-summability
title_full_unstemmed Korovkin second theorem via B-statistical A-summability
title_sort korovkin second theorem via b-statistical a-summability
publisher Hindawi Publishing Corporation
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30126/1/30126.pdf
http://psasir.upm.edu.my/id/eprint/30126/
http://www.hindawi.com/journals/aaa/2013/598963/
_version_ 1643829965383270400
score 13.211869

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