Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a funct...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2016/9121249 |
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| author | Shyam Lal Susheel Kumar |
| author_facet | Shyam Lal Susheel Kumar |
| author_sort | Shyam Lal |
| collection | DOAJ |
| description | A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα,0<α≤1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis. |
| format | Article |
| id | doaj-art-cd7ece7b3bd5498ca05d242b3f31f1ca |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cd7ece7b3bd5498ca05d242b3f31f1ca2025-08-20T02:19:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/91212499121249Quasi-Positive Delta Sequences and Their Applications in Wavelet ApproximationShyam Lal0Susheel Kumar1Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, IndiaA sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα,0<α≤1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis.http://dx.doi.org/10.1155/2016/9121249 |
| spellingShingle | Shyam Lal Susheel Kumar Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation International Journal of Mathematics and Mathematical Sciences |
| title | Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation |
| title_full | Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation |
| title_fullStr | Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation |
| title_full_unstemmed | Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation |
| title_short | Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation |
| title_sort | quasi positive delta sequences and their applications in wavelet approximation |
| url | http://dx.doi.org/10.1155/2016/9121249 |
| work_keys_str_mv | AT shyamlal quasipositivedeltasequencesandtheirapplicationsinwaveletapproximation AT susheelkumar quasipositivedeltasequencesandtheirapplicationsinwaveletapproximation |