Approximation of signals (functions) belonging to the weighted W ( L p, ξ ( t ) ) -class by linear operators

M. L. Mittal, B. E. Rhoades and Vishnu Narayan Mishra

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-10

Abstract:

Mittal and Rhoades (1999–2001) and Mittal et al. (2006) have initiated the studies of error estimates E n ( 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 ( L p , 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 ( N p ) -matrices.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:053538

DOI: 10.1155/IJMMS/2006/53538

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