Abstract
Various investigators such as Khan (1974), Chandra (2002), and Liendler (2005) have determined the degree of approximation of 2π-periodic signals (functions) belonging to Lip(α,r)class of functions through trigonometric Fourier approximation using different summability matrices with monotone rows. Recently, Mittal et al. (2007 and 2011) have obtained the degree of approximation of signals belonging to Lip(α,r)- class by general summability matrix, which generalize some of the results of Chandra (2002) and results of Leindler (2005), respectively. In this paper, we determine the degree of approximation of functions belonging to Lip αandW(Lr,ξ(t)) classes by using Cesáro-Nörlund(C1·Np)summability without monotonicity condition on{pn}, which in turn generalizes the results of Lal (2009). We also note some errors appearing in the paper of Lal (2009) and rectify them in the light of observations of Rhoades et al. (2011).
Highlights
For a given signal function f ∈ Lr : Lr 0, 2π, r ≥ 1, let sn f sn f ; x a0 2 n ak cos kx bk sin kx k1 n uk f ; x k01.1 denote the partial sum, called trigonometric polynomial of degree or order n, of the first n 1 terms of the Fourier series of f
K0 the Norlund Np means of the sequence sn f or Fourier series of f
We note that Nn f and tCn N f are trigonometric polynomials of degree or order n
Summary
For a given signal function f ∈ Lr : Lr 0, 2π , r ≥ 1, let sn f sn f ; x a0 2 n ak cos kx bk sin kx k1 n uk f ; x k0.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
