Trigonometric Approximation of Signals (Functions) Belonging to W(Lr, 𝜉(t)) Class by Matrix (C1·Np) Operator

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 Lipα and W L , 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 .