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 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 Trigonometric Approximation of Signals (Functions) Belonging toW(Lr, ξ(t))Class by Matrix(C1·Np)Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Uaday Singh ◽  
M. L. Mittal ◽  
Smita Sonker
Keyword(s):  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Monotonicity Condition ◽  
Approximation Of Functions ◽  
Periodic Signals ◽  
Summability Matrices ◽  
Approximation Of Signals ◽  
Summability Matrix ◽  
Class Of Functions ◽  
General Summability

Various investigators such as Khan (1974), Chandra (2002), and Liendler (2005) have determined the degree of approximation of 2π-periodic signals (functions) belonging to Lip(α,r)class of functions through trigonometric Fourier approximation using different summability matrices with monotone rows. Recently, Mittal et al. (2007 and 2011) have obtained the degree of approximation of signals belonging to Lip(α,r)- class by general summability matrix, which generalize some of the results of Chandra (2002) and results of Leindler (2005), respectively. In this paper, we determine the degree of approximation of functions belonging to Lip αandW(Lr,ξ(t)) classes by using Cesáro-Nörlund(C1·Np)summability without monotonicity condition on{pn}, which in turn generalizes the results of Lal (2009). We also note some errors appearing in the paper of Lal (2009) and rectify them in the light of observations of Rhoades et al. (2011).

Approximation of Signals in the Weighted Zygmund Class Via Euler-hausdorff Product Summability Mean of Fourier Series

2020 ◽  
Vol 87 (1-2) ◽  
pp. 22
Author(s):  
A. A. Das ◽  
S. K. Paikray ◽  
T Pradhan ◽  
H. Dutta
Keyword(s):  
Fourier Series ◽  
Order Of Convergence ◽  
Approximation Of Functions ◽  
Zygmund Class ◽  
Approximation Of Signals

Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class <em>W(Z<sub>r</sub><sup>(ω)</sup>)</em> by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.

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