On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(Lr , ξ(t))(r ⩾1)-class by matrix (C 1 ⋅ Np ) operator of conjugate series of its Fourier series.

Abstract: In the present paper, a new theorem on the degree of approximation of function conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz -class by dropping the monotonicity condition on the generating sequence {pn } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22]. [Copyright &y& Elsevier]