Approximation of signals of class Lip(α, p) by linear operators

Mittal, Rhoades [5-8] and Mittal et al. [9,10] have initiated a study of error estimates E-n(f) through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix T does not have monotone rows. In this paper we continue the work. Here we extend two theorems of Leindler [4], where he has weakened the conditions on {p(n)} given by Chandra [2], to more general classes of triangular matrix methods. Our Theorem also partially generalizes Theorem 4 of Mittal et al. [11] by dropping the monotonicity on the elements of matrix rows, which in turn generalize the results of Quade [15]. (C) 2010 Elsevier Inc. All rights reserved.