Korovkin Second Theorem via -Statistical -Summability
Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation pro...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/598963 |
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| author | M. Mursaleen A. Kiliçman |
| author_facet | M. Mursaleen A. Kiliçman |
| author_sort | M. Mursaleen |
| collection | DOAJ |
| description | Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval 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, , and in the space as well as for the functions 1, cos, and sin in the space of all continuous 2-periodic functions on the real line. In this paper, we use the notion of -statistical -summability to prove the Korovkin second approximation theorem. We also study the rate of -statistical -summability of a sequence of positive linear operators defined from into . |
| format | Article |
| id | doaj-art-c524c41c2e4a468684f8d37c76eb04ae |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c524c41c2e4a468684f8d37c76eb04ae2025-02-03T05:59:32ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/598963598963Korovkin Second Theorem via -Statistical -SummabilityM. Mursaleen0A. Kiliçman1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaKorovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval 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, , and in the space as well as for the functions 1, cos, and sin in the space of all continuous 2-periodic functions on the real line. In this paper, we use the notion of -statistical -summability to prove the Korovkin second approximation theorem. We also study the rate of -statistical -summability of a sequence of positive linear operators defined from into .http://dx.doi.org/10.1155/2013/598963 |
| spellingShingle | M. Mursaleen A. Kiliçman Korovkin Second Theorem via -Statistical -Summability Abstract and Applied Analysis |
| title | Korovkin Second Theorem via -Statistical -Summability |
| title_full | Korovkin Second Theorem via -Statistical -Summability |
| title_fullStr | Korovkin Second Theorem via -Statistical -Summability |
| title_full_unstemmed | Korovkin Second Theorem via -Statistical -Summability |
| title_short | Korovkin Second Theorem via -Statistical -Summability |
| title_sort | korovkin second theorem via statistical summability |
| url | http://dx.doi.org/10.1155/2013/598963 |
| work_keys_str_mv | AT mmursaleen korovkinsecondtheoremviastatisticalsummability AT akilicman korovkinsecondtheoremviastatisticalsummability |