On the degree of approximation of conjugate functions in weighted Lipschitz class

2014 ◽  
pp. 91-100
Keyword(s):  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Conjugate Functions

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 Summation-Integral Type Operators Based on Lupas-Jain Functions

2021 ◽  
Vol 45 (02) ◽  
pp. 309-322
Author(s):  
NESIBE MANAV ◽  
NURHAYAT ISPIR
Keyword(s):  
Modulus Of Continuity ◽  
Local Approximation ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Integral Type ◽  
Base Functions

We introduce a genuine summation-integral type operators based on Lupaş-Jain type base functions related to the unbounded sequences. We investigated their degree of approximation in terms of modulus of continuity and ????-functional for the functions from bounded and continuous functions space. Furthermore, we give some theorems for the local approximation properties of functions belonging to Lipschitz class. Also, we give Voronovskaja theorem for these operators.

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 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

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