Open AccessError bounds of a function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet and its applications in the approximation of functions
Author(s) -
Shyam Lal,
S. Kumar,
S.K. Mishra,
A.K. Awasthi
Publication year - 2022
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.14.1.29-48
Subject(s) - mathematics , chebyshev filter , chebyshev iteration , chebyshev nodes , wavelet , lipschitz continuity , chebyshev equation , chebyshev pseudospectral method , estimator , approximation theory , equioscillation theorem , mathematical analysis , mathematical optimization , computer science , statistics , gegenbauer polynomials , orthogonal polynomials , artificial intelligence , classical orthogonal polynomials
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.