A Note on Wavelet Approximation of Functions

Shyam Lal, Priya Kumari

Abstract

In this paper, a class Lip_α^(s)[0,1] is introduced. This class of functions is a generalization of known Lipschitz class Lip_α[0,1], 0 < α ≤ 1  of functions. Four new estimators E_N⁽¹⁾(f), E_J⁽²⁾(f), E_N⁽³⁾(f) and E_N⁽⁴⁾(f) of functions of Lip_α[0,1] and Lip_α^(s)[0,1] classes have been obtained. These estimators are sharper and best possible in the approximation of functions by wavelet methods.