On Strong Approximation in Generalized Hölder and Zygmund Spaces
The strong approximation of a function is a useful tool to analyze the convergence of its Fourier series. It is based on the summability techniques. However, unlike matrix summability methods, it uses non-linear methods to derive an auxiliary sequence using approximation errors generated by the seri...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Computer Sciences & Mathematics Forum |
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| Online Access: | https://www.mdpi.com/2813-0324/7/1/9 |
| _version_ | 1827575142803308544 |
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| author | Birendra Singh Uaday Singh |
| author_facet | Birendra Singh Uaday Singh |
| author_sort | Birendra Singh |
| collection | DOAJ |
| description | The strong approximation of a function is a useful tool to analyze the convergence of its Fourier series. It is based on the summability techniques. However, unlike matrix summability methods, it uses non-linear methods to derive an auxiliary sequence using approximation errors generated by the series under analysis. In this paper, we give some direct results on the strong means of Fourier series of functions in generalized Hölder and Zygmund spaces. To elaborate its use, we deduce some corollaries. |
| first_indexed | 2024-03-08T20:53:00Z |
| format | Article |
| id | doaj.art-a9616735e6774be395dee24ce044e587 |
| institution | Directory Open Access Journal |
| issn | 2813-0324 |
| language | English |
| last_indexed | 2024-03-08T20:53:00Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computer Sciences & Mathematics Forum |
| spelling | doaj.art-a9616735e6774be395dee24ce044e5872023-12-22T14:02:04ZengMDPI AGComputer Sciences & Mathematics Forum2813-03242023-04-0171910.3390/IOCMA2023-14433On Strong Approximation in Generalized Hölder and Zygmund SpacesBirendra Singh0Uaday Singh1School of Science, Maharishi University of Information Technology, Lucknow 226013, IndiaDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, IndiaThe strong approximation of a function is a useful tool to analyze the convergence of its Fourier series. It is based on the summability techniques. However, unlike matrix summability methods, it uses non-linear methods to derive an auxiliary sequence using approximation errors generated by the series under analysis. In this paper, we give some direct results on the strong means of Fourier series of functions in generalized Hölder and Zygmund spaces. To elaborate its use, we deduce some corollaries.https://www.mdpi.com/2813-0324/7/1/9approximationstrong meanssummabilityHölderZygmund |
| spellingShingle | Birendra Singh Uaday Singh On Strong Approximation in Generalized Hölder and Zygmund Spaces Computer Sciences & Mathematics Forum approximation strong means summability Hölder Zygmund |
| title | On Strong Approximation in Generalized Hölder and Zygmund Spaces |
| title_full | On Strong Approximation in Generalized Hölder and Zygmund Spaces |
| title_fullStr | On Strong Approximation in Generalized Hölder and Zygmund Spaces |
| title_full_unstemmed | On Strong Approximation in Generalized Hölder and Zygmund Spaces |
| title_short | On Strong Approximation in Generalized Hölder and Zygmund Spaces |
| title_sort | on strong approximation in generalized holder and zygmund spaces |
| topic | approximation strong means summability Hölder Zygmund |
| url | https://www.mdpi.com/2813-0324/7/1/9 |
| work_keys_str_mv | AT birendrasingh onstrongapproximationingeneralizedholderandzygmundspaces AT uadaysingh onstrongapproximationingeneralizedholderandzygmundspaces |