Statistical Approximation for Periodic Functions of Two Variables
We prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical summability (C,1,1). We also study the rate of statistical summability (C,1,1) of positive linear operators. Finally we construct an example to show that our result is stronger than thos...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/491768 |
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| _version_ | 1849306503151878144 |
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| author | Abdullah Alotaibi M. Mursaleen S. A. Mohiuddine |
| author_facet | Abdullah Alotaibi M. Mursaleen S. A. Mohiuddine |
| author_sort | Abdullah Alotaibi |
| collection | DOAJ |
| description | We prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical summability (C,1,1). We also study the rate of statistical summability (C,1,1) of positive linear operators. Finally we construct an example to show that our result is stronger than those previously proved for Pringsheim's convergence and statistical convergence. |
| format | Article |
| id | doaj-art-3422f3d4c6694ab298c513482d8cd7da |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-3422f3d4c6694ab298c513482d8cd7da2025-08-20T03:55:06ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/491768491768Statistical Approximation for Periodic Functions of Two VariablesAbdullah Alotaibi0M. Mursaleen1S. A. Mohiuddine2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical summability (C,1,1). We also study the rate of statistical summability (C,1,1) of positive linear operators. Finally we construct an example to show that our result is stronger than those previously proved for Pringsheim's convergence and statistical convergence.http://dx.doi.org/10.1155/2013/491768 |
| spellingShingle | Abdullah Alotaibi M. Mursaleen S. A. Mohiuddine Statistical Approximation for Periodic Functions of Two Variables Journal of Function Spaces and Applications |
| title | Statistical Approximation for Periodic Functions of Two Variables |
| title_full | Statistical Approximation for Periodic Functions of Two Variables |
| title_fullStr | Statistical Approximation for Periodic Functions of Two Variables |
| title_full_unstemmed | Statistical Approximation for Periodic Functions of Two Variables |
| title_short | Statistical Approximation for Periodic Functions of Two Variables |
| title_sort | statistical approximation for periodic functions of two variables |
| url | http://dx.doi.org/10.1155/2013/491768 |
| work_keys_str_mv | AT abdullahalotaibi statisticalapproximationforperiodicfunctionsoftwovariables AT mmursaleen statisticalapproximationforperiodicfunctionsoftwovariables AT samohiuddine statisticalapproximationforperiodicfunctionsoftwovariables |