A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices
In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1895 |
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| author | Hari M. Srivastava Khursheed J. Ansari Faruk Özger Zeynep Ödemiş Özger |
| author_facet | Hari M. Srivastava Khursheed J. Ansari Faruk Özger Zeynep Ödemiş Özger |
| author_sort | Hari M. Srivastava |
| collection | DOAJ |
| description | In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study. |
| first_indexed | 2024-03-10T08:36:57Z |
| format | Article |
| id | doaj.art-4955b2c187f94088ad698e38d93d6f5f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:36:57Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4955b2c187f94088ad698e38d93d6f5f2023-11-22T08:33:30ZengMDPI AGMathematics2227-73902021-08-01916189510.3390/math9161895A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite MatricesHari M. Srivastava0Khursheed J. Ansari1Faruk Özger2Zeynep Ödemiş Özger3Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Engineering Sciences, İzmir Katip Çelebi University, İzmir 35620, TurkeyDepartment of Engineering Sciences, İzmir Katip Çelebi University, İzmir 35620, TurkeyIn this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study.https://www.mdpi.com/2227-7390/9/16/1895four dimensional matrixdouble sequencepower series methodstatistical convergencecomputer graphicserror of approximation |
| spellingShingle | Hari M. Srivastava Khursheed J. Ansari Faruk Özger Zeynep Ödemiş Özger A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices Mathematics four dimensional matrix double sequence power series method statistical convergence computer graphics error of approximation |
| title | A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices |
| title_full | A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices |
| title_fullStr | A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices |
| title_full_unstemmed | A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices |
| title_short | A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices |
| title_sort | link between approximation theory and summability methods via four dimensional infinite matrices |
| topic | four dimensional matrix double sequence power series method statistical convergence computer graphics error of approximation |
| url | https://www.mdpi.com/2227-7390/9/16/1895 |
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