Chebyshev wavelet approximation of functions having first derivative of H$$\ddot{\text {o}}$$lder’s class

Abstract

In this paper, the Chebyshev wavelet approximations of a uniformly continuous function f and a functions f whose first derivative $$f'$$ of class $$H^\alpha [0,1), 0 < \alpha \le 1$$ , have been determined. These wavelet estimators are sharper, better and best possible in Wavelet analysis. A new method for solving differential equations by the Chebyshev wavelet method has been proposed. Lane-Emden and third-order pantograph non-linear differential equations have been solved by this method. The solutions of these equations have been compared by their exact solution. It is found that the exact solutions and solutions by the Chebyshev Wavelet method are nearly same. This is a significant achievement in wavelet analysis.