On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its fourier series

2011 ◽  
Vol 217 (16) ◽  
pp. 6868-6871 ◽  
Author(s):  
B.E. Rhoades ◽  
Kevser Ozkoklu ◽  
Inci Albayrak
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Hausdorff Means

scholarly journals ON THE DEGREE OF APPROXIMATION OF FUNCTIONS BELONGING TO THE LIPSCHITZ CLASS BY $(e,c)$ MEANS

1995 ◽  
Vol 26 (3) ◽  
pp. 225-229
Author(s):  
U. K. SHRIVASTAVA ◽  
S. K. VERMA
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Approximation Of Functions

In the present paper, we obtain the degree of approximation of $f\in$ Lip$\alpha$ ($0 <\alpha\le 1$) by ($e, c$) means ($c > 0$) of its Fourier Series.

scholarly journals On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series

2003 ◽  
Vol 34 (3) ◽  
pp. 245-247 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fourier Series ◽  
Series Representation ◽  
Triangular Matrix ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
The Matrix ◽  
Hausdorff Matrices ◽  
Cesàro Matrix ◽  
Hausdorff Means ◽  
Euler Matrix

In a recent paper Lal and Yadav [1] obtained a theorem on the degree of approximation for a function belonging to a Lipschitz class using a triangular matrix transform of the Fourier series representation of the function. The matrix involved was the product of $ (C, 1) $, the Cesaro matrix of order one, with $ (E, 1) $, the Euler matrix of order one. In this paper we extend this result to a much wider class of Hausdorff matrices.

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.

scholarly journals On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jitendra Kumar Kushwaha
Keyword(s):  
Fourier Series ◽  
Approximation Theory ◽  
Lipschitz Function ◽  
Applied Mathematics ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Conjugate Series ◽  
Important Field

Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler’s mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler’s means of conjugate of functions belonging to class has been obtained. and classes are the particular cases of class. The main result of this paper generalizes some well-known results in this direction.

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 On approximation in generalized Zygmund class

2019 ◽  
Vol 52 (1) ◽  
pp. 370-387
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Conjugate Function ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
Product Method ◽  
Hausdorff Means

AbstractHere, we estimate the degree of approximation of a conjugate function {\tilde g} and a derived conjugate function {\tilde g'} , of a 2π-periodic function g \in Z_r^\lambda , r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.

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