Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm
Mittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimates En(f) through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix T does not have monotone rows. In this paper, the first author continues the work in the direc...
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| Format: | Article |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/267383 |
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| author | M. L. Mittal Mradul Veer Singh |
| author_facet | M. L. Mittal Mradul Veer Singh |
| author_sort | M. L. Mittal |
| collection | DOAJ |
| description | Mittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimates En(f) through
trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix T does not have monotone rows. In this paper, the first author continues the work in the direction for T to be a Np-matrix. We extend two theorems on summability matrix Np of Deger et al. (2012) where they have extended two theorems of Chandra (2002) using Cλ-method obtained by deleting a set of rows from Cesàro matrix C1. Our theorems also generalize two theorems of Leindler (2005) to Np-matrix which in turn generalize the result of Chandra (2002) and Quade (1937). |
| format | Article |
| id | doaj-art-a02da608ad1e439a9b6387585a69b223 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a02da608ad1e439a9b6387585a69b2232025-02-03T06:10:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/267383267383Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-NormM. L. Mittal0Mradul Veer Singh1Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, IndiaDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, IndiaMittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimates En(f) through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix T does not have monotone rows. In this paper, the first author continues the work in the direction for T to be a Np-matrix. We extend two theorems on summability matrix Np of Deger et al. (2012) where they have extended two theorems of Chandra (2002) using Cλ-method obtained by deleting a set of rows from Cesàro matrix C1. Our theorems also generalize two theorems of Leindler (2005) to Np-matrix which in turn generalize the result of Chandra (2002) and Quade (1937).http://dx.doi.org/10.1155/2014/267383 |
| spellingShingle | M. L. Mittal Mradul Veer Singh Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm International Journal of Mathematics and Mathematical Sciences |
| title | Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm |
| title_full | Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm |
| title_fullStr | Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm |
| title_full_unstemmed | Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm |
| title_short | Approximation of Signals (Functions) by Trigonometric Polynomials in Lp-Norm |
| title_sort | approximation of signals functions by trigonometric polynomials in lp norm |
| url | http://dx.doi.org/10.1155/2014/267383 |
| work_keys_str_mv | AT mlmittal approximationofsignalsfunctionsbytrigonometricpolynomialsinlpnorm AT mradulveersingh approximationofsignalsfunctionsbytrigonometricpolynomialsinlpnorm |