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

被引：0

作者：

Lal, S. ^{[1
]}

Kumar, S. ^{[2
]}

Mishra, S. K. ^{[2
]}

Awasthi, A. K. ^{[2
]}

机构：

[1] Banaras Hindu Univ, Inst Sci, Dept Math, Varanasi 221005, Uttar Pradesh, India

[2] Tilak Dhari Post Grad Coll, Fac Sci, Dept Math, Jaunpur 222002, India

来源：

CARPATHIAN MATHEMATICAL PUBLICATIONS | 2022年 / 14卷 / 01期

关键词：

Li-[0; Li-1)alpha class of functions; Lip([0,1))xi class of functions; wavelet; multiresolution analysis; pseudo-Chebyshev function; pseudo-Chebyshev wavelet; OPERATIONAL MATRIX; SAMPLING THEORY; APPROXIMATION; EQUATIONS; PROPAGATION;

D O I：

10.15330/cmp.14.1.29-48

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：29 / 48

页数：20

共 6 条

[1] Approximation of a Function f of Generalized Lipschitz Class by Its Extended Legendre Wavelet Series
Lal S.
Kumari P.
International Journal of Applied and Computational Mathematics, 2018, 4 (6)
[2] Estimation of approximation error of a function having its derivatives belonging to Lipschitz class of order- α by extended Legendre wavelet (ELW) method and its applications
Sharma, Vivek Kumar
Singh, Sonoo
Pandey, Rajesh
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FILOMAT, 2024, 38 (01) : 67 - 98
[3] Wavelet approximation of functions belonging to generalized lipschitz class by extended haar wavelet series and its application in the solution of bessel differential equation using haar operational matrix
Lal S.
Kumari P.
International Journal of Applied and Computational Mathematics, 2019, 5 (3)
[4] Approximations of a function whose first and second derivatives belonging to generalized Holder's class by extended Legendre wavelet method and its applications in solutions of differential equations
Lal, Shyam
Priya, Sharma R.
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2021, 70 (02) : 959 - 993
[5] Approximations of a function whose first and second derivatives belonging to generalized Hölder’s class by extended Legendre wavelet method and its applications in solutions of differential equations
Shyam Lal
Priya R. Sharma
Rendiconti del Circolo Matematico di Palermo Series 2, 2021, 70 : 959 - 993
[6] Approximation of Functions Belonging to Generalized Hölder’s Class Hα(ω)[0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\alpha }^{(\omega )}[0,1)$$\end{document} by First Kind Chebyshev Wavelets and Its Applications in the Solution of Linear and Nonlinear Differential Equations
Shyam Lal
Indra Bhan
International Journal of Applied and Computational Mathematics, 2019, 5 (6)

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