Error bounds of a function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet and its applications in the approximation of functions

Abstract

In this paper, a new computation method derived to solve the problems of approximation theory. This method is based upon pseudo-Chebyshev wavelet approximations. The pseudo-Chebyshev wavelet is being presented for the first time. The pseudo-Chebyshev wavelet is constructed by the pseudo-Chebyshev functions. The method is described and after that the error bounds of a function is analyzed. We have illustrated an example to demonstrate the accuracy and efficiency of the pseudo-Chebyshev wavelet approximation method and the main results. Four new error bounds of the function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet are obtained. These estimators are the new fastest and best possible in theory of wavelet analysis.

Keywords

• lip${}_{[0,1)}\alpha$ class of functions
• lip${}_{[0,1)}\xi$ class of functions
• wavelet
• multiresolution analysis
• pseudo-chebyshev function
• pseudo-chebyshev wavelet