Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators
Mittal and Rhoades (1999–2001) and Mittal et al. (2006) have initiated the studies of error estimates En(f) through trigonometric Fourier approximations (TFA) for the situations in which the summability matrix T does not have monotone rows. In this paper, we determine the degree of approximation of...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/53538 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849401314439593984 |
|---|---|
| author | M. L. Mittal B. E. Rhoades Vishnu Narayan Mishra |
| author_facet | M. L. Mittal B. E. Rhoades Vishnu Narayan Mishra |
| author_sort | M. L. Mittal |
| collection | DOAJ |
| description | Mittal and Rhoades (1999–2001) and Mittal et al. (2006) have initiated the studies of error estimates En(f) through trigonometric Fourier approximations (TFA) for the situations in which the summability matrix T does not have monotone rows. In this paper, we determine the degree of approximation of a function f˜, conjugate to a periodic function f belonging to the weighted W(Lp,ξ(t))-class (p≥1), where ξ(t) is nonnegative and increasing function of t by matrix operators T (without monotone rows) on a conjugate series of Fourier series associated with f. Our theorem extends a recent result of Mittal et al. (2005) and a theorem of Lal and Nigam (2001) on general matrix summability. Our theorem also generalizes the results of Mittal, Singh, and Mishra (2005) and Qureshi (1981-1982) for Nörlund (Np)-matrices. |
| format | Article |
| id | doaj-art-84d47add73a843079e86d35998b21c2d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-84d47add73a843079e86d35998b21c2d2025-08-20T03:37:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/5353853538Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operatorsM. L. Mittal0B. E. Rhoades1Vishnu Narayan Mishra2Department of Mathematics, IIT Roorkee, Roorkee, Uttaranchal 247667, IndiaDepartment of Mathematics, Indiana University, Bloomington, IN 47405, USADepartment of Mathematics, IIT Roorkee, Roorkee, Uttaranchal 247667, IndiaMittal and Rhoades (1999–2001) and Mittal et al. (2006) have initiated the studies of error estimates En(f) through trigonometric Fourier approximations (TFA) for the situations in which the summability matrix T does not have monotone rows. In this paper, we determine the degree of approximation of a function f˜, conjugate to a periodic function f belonging to the weighted W(Lp,ξ(t))-class (p≥1), where ξ(t) is nonnegative and increasing function of t by matrix operators T (without monotone rows) on a conjugate series of Fourier series associated with f. Our theorem extends a recent result of Mittal et al. (2005) and a theorem of Lal and Nigam (2001) on general matrix summability. Our theorem also generalizes the results of Mittal, Singh, and Mishra (2005) and Qureshi (1981-1982) for Nörlund (Np)-matrices.http://dx.doi.org/10.1155/IJMMS/2006/53538 |
| spellingShingle | M. L. Mittal B. E. Rhoades Vishnu Narayan Mishra Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators International Journal of Mathematics and Mathematical Sciences |
| title | Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators |
| title_full | Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators |
| title_fullStr | Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators |
| title_full_unstemmed | Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators |
| title_short | Approximation of signals (functions) belonging to the weighted W(Lp,ξ(t))-class by linear operators |
| title_sort | approximation of signals functions belonging to the weighted w lp ξ t class by linear operators |
| url | http://dx.doi.org/10.1155/IJMMS/2006/53538 |
| work_keys_str_mv | AT mlmittal approximationofsignalsfunctionsbelongingtotheweightedwlpxtclassbylinearoperators AT berhoades approximationofsignalsfunctionsbelongingtotheweightedwlpxtclassbylinearoperators AT vishnunarayanmishra approximationofsignalsfunctionsbelongingtotheweightedwlpxtclassbylinearoperators |