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 Norlund (Np)-matrices.
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