On the degree of approximation of functions in a weighted Lipschitz class by almost matrix summability method

2017 ◽  
Vol 28 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Arti Rathore ◽  
Uaday Singh
Keyword(s):  
Degree Of Approximation ◽  
Summability Method ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Matrix Summability

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 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 Approximation of functions belonging to LIP (α, p) class by (E, 1)(N,pn) means of its fourier series

1970 ◽  
Vol 7 (1) ◽  
pp. 1-8
Author(s):  
Binod Prasad Dhakal
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Subject Classification ◽  
Approximation Of Functions ◽  
Keywords And Phrases ◽  
Approximation Of A Function

The present paper deals with approximation of a function belonging to the Lip (α, p) class by product summability method. Here product of Euler (E,1) summability method and Nörlund (N, pn) method has been taken. A new estimate on degree of approximation of a function f belonging to Lip (α, p) class has been determined by (E,1) (N, pn) summability of a Fourier series. Subject Classification: 40G05, 42B05, 42B08 Keywords and phrases: Degree of approximation; (E,1)(N, pn) summability; Fourier series; Lip (α, p) class; Lp norm.DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5416 KUSET 2011; 7(1): 1-8

scholarly journals On the approximation of function belonging to weighted $ {(L^p, \xi(t))}$ class by almost matrix summability method of its Fourier series

2004 ◽  
Vol 35 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Shyam Lal
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Matrix Summability ◽  
Approximation Of Function

In this paper, the degree of approximation of function belonging to weighted $ W(L^p$, $ \xi(t))$ class by almost matrix summability of its Fourier series has been determined. The main theorem improves all the previously known theorems in this line of work.

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.

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