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

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Shyam Lal ◽  
Priya Kumari
Keyword(s):  
Lipschitz Class ◽  
Generalized Lipschitz Class ◽  
Approximation Of A Function ◽  
Wavelet Series

scholarly journals Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abhishek Mishra ◽  
Vishnu Narayan Mishra ◽  
M. Mursaleen
Keyword(s):  
Double Fourier Series ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Gamma Delta ◽  
Approximation Of Functions ◽  
Matrix Summability ◽  
Alpha Beta ◽  
Generalized Lipschitz Class ◽  
Hausdorff Matrix

AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

scholarly journals Approximation of signals belonging to generalized Lipschitz class using -summability mean of Fourier series

2016 ◽  
Vol 3 (1) ◽  
pp. 1250343 ◽  
Author(s):  
Tejaswini Pradhan ◽  
Susanta Kumar Paikray ◽  
Umakanta Misra ◽  
Hari M. Srivastava
Keyword(s):  
Fourier Series ◽  
Lipschitz Class ◽  
Approximation Of Signals ◽  
Generalized Lipschitz Class

scholarly journals Approximation of a generalized Lipschitz class function by Euler - Cesàro means of Fourier series

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 151-158
Author(s):  
Binod Prasad Dhakal
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Summability Methods ◽  
Class Function ◽  
Cesáro Means ◽  
Generalized Lipschitz Class ◽  
Cesàro Method

In this paper, I have taken product of two summability methods, Euler and Cesaro; and establish a new theorem on the degree of approximation of the function f belonging to W(Lp, ?(t)) classes by Euler - Cesaro method. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7190 BIBECHANA 9 (2013) 151-158

Lipschitz classes and convolution approximation processes

1981 ◽  
Vol 90 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Z. Ditzian
Keyword(s):  
Continuous Function ◽  
Asymptotic Behaviour ◽  
Lipschitz Class ◽  
Equivalence Relations ◽  
Approximation Process ◽  
Lipschitz Classes ◽  
Image Position ◽  
Generalized Lipschitz Class

For a continuous function f(x) on the reals or on the circle T (continuous and 2π periodic) we say that f(x) belongs to the generalized Lipschitz class, denoted by f ∈ Lip* α, ifwhere and Δhf(x) = f(x + ½h)−f(x−½h). For a convolution approximation process given bywherewe shall investigate equivalence relations between the asymptotic behaviour of (d/dx)rAn(f, x) and f ∈ Lip* α.

scholarly journals The degree of approximation by Hausdorff means of a conjugate Fourier series

2016 ◽  
Vol 70 (2) ◽  
pp. 63
Author(s):  
Sergiusz Kęska
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Conjugate Series ◽  
Conjugate Fourier Series ◽  
Hausdorff Means ◽  
Approximation Of A Function

The purpose of this paper is to analyze the degree of approximation of a function \(\overline f\) that is a conjugate of a function \(f\) belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.

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