标题：Approximation of signals (functions) belonging to the weighted
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>-class by linear operators
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2006
卷号：2006
DOI：10.1155/IJMMS/2006/53538
出版社：Hindawi Publishing Corporation
摘要：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.
