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

Given a function f in the class Lip(α,p) , 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.