scholarly journals Euler-Hausdorff matrix summability operator and trigonometric approximation of the conjugate of a function belonging to the generalized Lipschitz class

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Shyam Lal ◽  
Abhishek Mishra
Keyword(s):  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Matrix Summability ◽  
Generalized Lipschitz Class ◽  
Hausdorff Matrix

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 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
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