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

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.