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 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 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.

scholarly journals Degree of approximation of conjugate of $ {Lip(\alpha,p)}$ function by ${(C,1)}$ ${(E,1)}$ means of conjugate of a Fourier series

2002 ◽  
Vol 33 (3) ◽  
pp. 269-274 ◽  
Author(s):  
Shyam Lal ◽  
Prem Narain Singh
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series

An estimate of degree of approximation of conjugates of Lip$ (\alpha, p)$ functions by ($ C$,1) ($ E$,1) product means of conjugate series of a Fourier Series is obtained.

scholarly journals Degree of approximation of a function by Nörlund means of its Fourier series

1981 ◽  
Vol 23 (3) ◽  
pp. 395-412
Author(s):  
R. B. Saxena
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Nörlund Means ◽  
Cesáro Means ◽  
Approximation Of A Function

Two theorems of T.M. Flett [Quart. J. Math. Oxford Ser. (2) 7 (1956), 81–95] on the degree of approximation to a function by the Cesàro means of its Fourier series are extended to Nörlund means. Their conjugate analogues are also proved.

scholarly journals The degree of approximation of functions, and their conjugates, belonging to several general Lipschitz classes, by Hausdorff matrix means of their Fourier series and conjugate series of their Fourier series

2014 ◽  
Vol 45 (4) ◽  
pp. 389-395 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Approximation Of Functions ◽  
Conjugate Series ◽  
Lipschitz Classes ◽  
Matrix Means ◽  
Hausdorff Matrix ◽  
Matrix Approximations

In this paper Hausdorff matrix approximations are obtained for a function and its conjugate belonging to any one of several generalized Lipschitz classes.

scholarly journals Approximation of signals (functions) belonging to the weightedW(Lp,ξ(t))-class by linear operators

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
M. L. Mittal ◽  
B. E. Rhoades ◽  
Vishnu Narayan Mishra
Keyword(s):  
Degree Of Approximation ◽  
Linear Operators ◽  
Conjugate Series ◽  
General Matrix ◽  
Matrix Summability ◽  
Approximation Of Signals ◽  
Summability Matrix ◽  
Matrix Operators ◽  
Increasing Function ◽  
Approximation Of A Function

Mittal and Rhoades (1999–2001) and Mittal et al. (2006) have initiated the studies of error estimatesEn(f)through trigonometric Fourier approximations (TFA) for the situations in which the summability matrixTdoes not have monotone rows. In this paper, we determine the degree of approximation of a functionf˜, conjugate to a periodic functionfbelonging to the weightedW(Lp,ξ(t))-class(p≥1), whereξ(t)is nonnegative and increasing function oftby matrix operatorsT(without monotone rows) on a conjugate series of Fourier series associated withf. Our theorem extends a recent result of Mittal et al. (2005) and a theorem of Lal and Nigam (2001) on general matrix summability. Our theorem also generalizes the results of Mittal, Singh, and Mishra (2005) and Qureshi (1981-1982) for Nörlund(Np)-matrices.

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