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

Autor: Vishnu Narayan Mishra, Kejal Khatri, Lakshmi Narayan Mishra, Deepmala
Rok vydání: 2014
Předmět:
Zdroj: Applied Mathematics and Computation. 237:252-263
ISSN: 0096-3003
DOI: 10.1016/j.amc.2014.03.085
Popis: In the present paper, a new theorem on the degree of approximation of function f ∼ , conjugate to a 2 π periodic function f belonging to the generalized weighted Lipschitz W ( L r , ξ ( t ) ) ( r ⩾ 1 ) -class by dropping the monotonicity condition on the generating sequence { p n } 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].
Databáze: OpenAIRE