Approximation of signals (functions) of Lip(α, p), (p > 1)-class by trigonometric polynomials

Abstract

Given a function f in the class Lip(α,p) (0 < α ≤ 1, p > 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the nth terms of either certain Riesz mean or Nцrlund mean transforms of the Fourier series representation for f. They showed that the degree of approximation is O((λ(n))−α) and extended two theorems of Leindler (2005) where he had weakened the conditions on {pn} given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices.