Legendre Wavelet approximation of functions having derivatives of Lipschitz class

Abstract

In this paper, Legendre Wavelet approximation of functions f having first derivative f' and second derivative f" of Lipα class, 0 <  α ≤ 1, have been determined. These wavelet estimators are sharper, better and best possible in Wavelet Analysis. It is observed that the Legendre Wavelet estimator of f whose f" belongs to Lipα is sharper than the estimator of f having f' belongs to Lipα class.