Approximation of Functions of Bounded Derivatives by Legendre Wavelet Method

Abstract

In this paper, we have established two new theorems  on wavelet approximation of a function $f$ with $0<\vert f^{v}(x)\vert<\infty$\quad $\forall x\in[0,1]$.  Four new estimates $E_{2^{i-1},0}^{(1)}$,$E_{2^{i-1},1}^{(2)}$,$E_{2^{i-1},2}^{(3)}$ and $E_{2^{i-1},M}^{(4)}$ of any function $f$ on $[0,1)$ having bounded derivatives are calculated by Legendre Wavelet Method.