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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/350474 |
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| _version_ | 1832548157095936000 |
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| author | Mohammed A. Alghamdi |
| author_facet | Mohammed A. Alghamdi |
| author_sort | Mohammed A. Alghamdi |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e8492a72a85f44b1978fe05e4c1de8a2 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e8492a72a85f44b1978fe05e4c1de8a22025-02-03T06:42:10ZengWileyJournal 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 |
| spellingShingle | Mohammed A. Alghamdi Approximation Theorems for Functions of Two Variables via σ-Convergence Journal of Function Spaces |
| title | 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_short | Approximation Theorems for Functions of Two Variables via σ-Convergence |
| title_sort | approximation theorems for functions of two variables via σ convergence |
| url | http://dx.doi.org/10.1155/2014/350474 |
| work_keys_str_mv | AT mohammedaalghamdi approximationtheoremsforfunctionsoftwovariablesviasconvergence |