On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(Lr, ξ(t))(r ⩾ 1)-class by matrix (C1 ⋅ Np) operator of conjugate series of its Fourier series

In the present paper, a new theorem on the degree of approximation of function f∼, conjugate to a 2π periodic function f   belonging to the generalized weighted Lipschitz W(Lr,ξ(t))(r⩾1)W(Lr,ξ(t))(r⩾1)-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].