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

Mittal and Rhoades (1999–2001) andMittal 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, andMishra (2005) and Qureshi (1981-1982) for Nörlund (Np)-matrices.