Using infinite matrices to approximate functions of class Lip(α,p) using trigonometric polynomials

Given a function f in the class Lip(α,p) (0 < α 1, p 1), Chandra [P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002) 13–26] approximated such an f by using trigonometric polynomials, which are the nth terms of either certain weighted mean or Nörlund mean transforms of the Fourier series representation for f . He showed that the degree of its approximation is O(n−α). In this paper we obtain the same degree of approximation for a more general class of lower triangular matrices, and deduce some of the results of [P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002) 13–26] as corollaries. © 2006 Elsevier Inc. All rights reserved