Approximation by weighted means of Walsh-Fourier series
We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p) by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1). We also note t...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000014 |
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| _version_ | 1832553190024806400 |
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| author | F. Móricz B. E. Rhoades |
| author_facet | F. Móricz B. E. Rhoades |
| author_sort | F. Móricz |
| collection | DOAJ |
| description | We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p) by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions. |
| format | Article |
| id | doaj-art-4fdc02aafa5747c2a03f3128fd8d9330 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4fdc02aafa5747c2a03f3128fd8d93302025-02-03T05:54:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-011911810.1155/S0161171296000014Approximation by weighted means of Walsh-Fourier seriesF. Móricz0B. E. Rhoades1Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6720, HungaryDepartment of Mathematics, Indiana University, Bloomington 47405, Indiana, USAWe study the rate of approximation to functions in Lp and, in particular, in Lip(α,p) by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.http://dx.doi.org/10.1155/S0161171296000014Walsh systemWalsh-Fourier seriesweighted meanrate of convergenceLipschitz classWalsh-Dirichlet kernelWalsh-Fejér kernelquasi-positive kernel. |
| spellingShingle | F. Móricz B. E. Rhoades Approximation by weighted means of Walsh-Fourier series International Journal of Mathematics and Mathematical Sciences Walsh system Walsh-Fourier series weighted mean rate of convergence Lipschitz class Walsh-Dirichlet kernel Walsh-Fejér kernel quasi-positive kernel. |
| title | Approximation by weighted means of Walsh-Fourier series |
| title_full | Approximation by weighted means of Walsh-Fourier series |
| title_fullStr | Approximation by weighted means of Walsh-Fourier series |
| title_full_unstemmed | Approximation by weighted means of Walsh-Fourier series |
| title_short | Approximation by weighted means of Walsh-Fourier series |
| title_sort | approximation by weighted means of walsh fourier series |
| topic | Walsh system Walsh-Fourier series weighted mean rate of convergence Lipschitz class Walsh-Dirichlet kernel Walsh-Fejér kernel quasi-positive kernel. |
| url | http://dx.doi.org/10.1155/S0161171296000014 |
| work_keys_str_mv | AT fmoricz approximationbyweightedmeansofwalshfourierseries AT berhoades approximationbyweightedmeansofwalshfourierseries |