Approximation of a Function f of Generalized Lipschitz Class by Its Extended Legendre Wavelet Series

被引：0
|
作者：
Lal S. [1 ]
Kumari P. [1 ]
机构：
[1] Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi
来源：
International Journal of Applied and Computational Mathematics | 2018年 / 4卷 / 6期
关键词：
Extended Legendre approximation; Extended Legendre expansion; Extended Legendre wavelet; Legendre wavelet; Lip; !sub]α[!/sub; !sup](s)[!/sup; 1); class; Lipξ[0;
D O I：
10.1007/s40819-018-0577-8
中图分类号：
学科分类号：
摘要：
In this paper, two classes Lipα(s)[0,1) and Lipξ[0 , 1) are introduced. These classes of functions are the generalization of the known Lipschitz class Lip α [0 , 1) , 0 < α≤ 1 of functions. Four new estimators Eμk,0(α)(f), Eμk,1(α)(f), Eμk,2(α)(f) and Eμk,M(α)(f) of functions of Lipα(s)[0,1) class and Eμk,0(ξ)(f),Eμk,1(ξ)(f), Eμk,2(ξ)(f) and Eμk,M(ξ)(f) of functions of Lipξ[0 , 1) class have been obtained. Five corollaries are deduced from the main theorems. These estimators are best possible in approximation of functions by wavelet methods. © 2018, Springer Nature India Private Limited.
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