scholarly journals The degree of approximation by Hausdorff means of a conjugate Fourier series

2016 ◽  
Vol 70 (2) ◽  
pp. 63
Author(s):  
Sergiusz Kęska
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Conjugate Series ◽  
Conjugate Fourier Series ◽  
Hausdorff Means ◽  
Approximation Of A Function

The purpose of this paper is to analyze the degree of approximation of a function \(\overline f\) that is a conjugate of a function \(f\) belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.

scholarly journals On approximation in generalized Zygmund class

2019 ◽  
Vol 52 (1) ◽  
pp. 370-387
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Conjugate Function ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
Product Method ◽  
Hausdorff Means

AbstractHere, we estimate the degree of approximation of a conjugate function {\tilde g} and a derived conjugate function {\tilde g'} , of a 2π-periodic function g \in Z_r^\lambda , r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.

scholarly journals On Degree of Approximation by Product Means of Conjugate Series of a Fourier Series

2012 ◽  
Vol 4 ◽  
pp. 5-11 ◽  
Author(s):  
S.K. Paikray ◽  
R.K. Jati ◽  
N.C. Sahoo ◽  
U.K. Misra
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Approximation Of A Function

In this paper a theorem on degree of approximation of a function f ∈ Lip(α, r) by product summability (E, q)(N, pn) of conjugate series of Fourier series associated with f has been established.

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 Degree of approximation of conjugate of a function belonging toLip(ξ(t),p)class by matrix summability means of conjugate Fourier series

2001 ◽  
Vol 27 (9) ◽  
pp. 555-563 ◽  
Author(s):  
Shyam Lal ◽  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Conjugate Fourier Series ◽  
Matrix Summability

We determine the degree of approximation of conjugate of a function belonging toLip(ξ(t),p)class by matrix summability means of a conjugate series of a Fourier 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 Approximation of a Function Belonging to Lip ((α, r) Class by Np,q. C1 Summability Method of its Fourier Series

2014 ◽  
Vol 14 (2) ◽  
pp. 117-122 ◽  
Author(s):  
JP Kushwaha ◽  
BP Dhakal
Keyword(s):  
Fourier Series ◽  
Science And Technology ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Approximation Of A Function

In this paper, an estimate for the degree of approximation of a function belonging to Lip(α, r) class by product summability method Np.q.C1 of its Fourier series has been established. DOI: http://dx.doi.org/10.3126/njst.v14i2.10424 Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 117-122

scholarly journals On the degree of approximation of conjugate of a function belonging to weighted $ W(L^p,\xi(t))$ class by matrix summability means of conjugate series of a Fourier series

2000 ◽  
Vol 31 (4) ◽  
pp. 279-288 ◽  
Author(s):  
Shyam Lal
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Matrix Summability

In this paper a new theorem on the degree of approximation of conjugate of a function belonging to weighted $ W(L^p,\xi(t))$ class by Matrix summability means of conjugate series of a Fourier series has been established. The main theorem is a generalization of serveral known and unknown results.

scholarly journals Degree of Approximation of Functionsf~∈HωClass by the(Np·E1)Means in the Hölder Metric

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Kejal Khatri
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Hölder Metric ◽  
Approximation Of A Function

A new estimate for the degree of approximation of a functionf˜∈Hωclass by(Np·E1)means of its Fourier series has been determined. Here, we extend the results of Singh and Mahajan (2008) which in turn generalize the result of Lal and Yadav (2001). Some corollaries have also been deduced from our main theorem.

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