scholarly journals Trigonometric approximation of functions belonging to Lipschitz class by matrix ( C 1 ⋅ N p ) operator of conjugate series of Fourier series

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
Vishnu Narayan Mishra ◽  
Vaishali Sonavane
Keyword(s):  
Fourier Series ◽  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Conjugate 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 Applications of Cesàro Submethod to Trigonometric Approximation of Signals (Functions) Belonging to ClassLip(α,p)inLp-Norm

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. L. Mittal ◽  
Mradul Veer Singh
Keyword(s):  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Approximation Of Signals

We prove two Theorems on approximation of functions belonging to Lipschitz classLip(α,p)inLp-norm using Cesàro submethod. Further we discuss few corollaries of our Theorems and compare them with the existing results. We also note that our results give sharper estimates than the estimates in some of the known results.

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.

Sign in / Sign up

Export Citation Format

Share Document