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

Authors

  • S. Lal Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
  • S. Kumar Department of Mathematics, Faculty of Science, Tilak Dhari Post Graduate College, Jaunpur-222002, India
  • S.K. Mishra Department of Mathematics, Faculty of Science, Tilak Dhari Post Graduate College, Jaunpur-222002, India
  • A.K. Awasthi Department of Mathematics, Faculty of Science, Tilak Dhari Post Graduate College, Jaunpur-222002, India
https://doi.org/10.15330/cmp.14.1.29-48

Keywords:

Lip${}_{[0,1)}\alpha$ class of functions, Lip${}_{[0,1)}\xi$ class of functions, wavelet, multiresolution analysis, pseudo-Chebyshev function, pseudo-Chebyshev wavelet
Published online: 2022-04-04

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.

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How to Cite
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Lal, S.; Kumar, S.; Mishra, S.; Awasthi, A. Error Bounds of a Function Related to Generalized Lipschitz Class via the Pseudo-Chebyshev Wavelet and Its Applications in the Approximation of Functions. Carpathian Math. Publ. 2022, 14, 29-48.