Convergence of generalized sampling series in weighted spaces
The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0014 |
| _version_ | 1811236509860233216 |
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| author | Acar Tuncer Alagöz Osman Aral Ali Costarelli Danilo Turgay Metin Vinti Gianluca |
| author_facet | Acar Tuncer Alagöz Osman Aral Ali Costarelli Danilo Turgay Metin Vinti Gianluca |
| author_sort | Acar Tuncer |
| collection | DOAJ |
| description | The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained. |
| first_indexed | 2024-04-12T12:10:45Z |
| format | Article |
| id | doaj.art-e78b8068e2d542e79e898920d0299649 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-04-12T12:10:45Z |
| publishDate | 2022-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-e78b8068e2d542e79e898920d02996492022-12-22T03:33:36ZengDe GruyterDemonstratio Mathematica2391-46612022-05-0155115316210.1515/dema-2022-0014Convergence of generalized sampling series in weighted spacesAcar Tuncer0Alagöz Osman1Aral Ali2Costarelli Danilo3Turgay Metin4Vinti Gianluca5Department of Mathematics, Selcuk University, Faculty of Science, Selcuklu, 42003, Konya, TurkeyDepartment of Mathematics, Bilecik Seyh Edebali University, Faculty of Science, Bilecik, TurkeyDepartment of Mathematics, Kirikkale University, Faculty of Science and Arts, Yahsihan, 71450, Kirikkale, TurkeyDepartment of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, ItalyDepartment of Mathematics, Selcuk University, Faculty of Science, Selcuklu, 42003, Konya, TurkeyDepartment of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, ItalyThe present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.https://doi.org/10.1515/dema-2022-0014generalized sampling operatorsweighted spacesweighted modulus of continuityvoronovskaja-type theoremquantitative order of approximation41a2541a35 |
| spellingShingle | Acar Tuncer Alagöz Osman Aral Ali Costarelli Danilo Turgay Metin Vinti Gianluca Convergence of generalized sampling series in weighted spaces Demonstratio Mathematica generalized sampling operators weighted spaces weighted modulus of continuity voronovskaja-type theorem quantitative order of approximation 41a25 41a35 |
| title | Convergence of generalized sampling series in weighted spaces |
| title_full | Convergence of generalized sampling series in weighted spaces |
| title_fullStr | Convergence of generalized sampling series in weighted spaces |
| title_full_unstemmed | Convergence of generalized sampling series in weighted spaces |
| title_short | Convergence of generalized sampling series in weighted spaces |
| title_sort | convergence of generalized sampling series in weighted spaces |
| topic | generalized sampling operators weighted spaces weighted modulus of continuity voronovskaja-type theorem quantitative order of approximation 41a25 41a35 |
| url | https://doi.org/10.1515/dema-2022-0014 |
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