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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30126/1/30126.pdf |
| _version_ | 1825947645754998784 |
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| author | Mursaleen, Mohammad Kilicman, Adem |
| author_facet | Mursaleen, Mohammad Kilicman, Adem |
| author_sort | Mursaleen, Mohammad |
| collection | UPM |
| 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). |
| first_indexed | 2024-03-06T08:16:34Z |
| format | Article |
| id | upm.eprints-30126 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:16:34Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Mursaleen, Mohammad Kilicman, Adem Korovkin second theorem via B-statistical A-summability |
| title | 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_short | Korovkin second theorem via B-statistical A-summability |
| title_sort | korovkin second theorem via b statistical a summability |
| url | http://psasir.upm.edu.my/id/eprint/30126/1/30126.pdf |
| work_keys_str_mv | AT mursaleenmohammad korovkinsecondtheoremviabstatisticalasummability AT kilicmanadem korovkinsecondtheoremviabstatisticalasummability |