Degree of Approximation by the $$ \left( {T.\,E^{\,1} } \right) $$ T . E 1 Means of Conjugate Series of Fourier Series in the Hölder Metric

2018 ◽  
Vol 43 (4) ◽  
pp. 1591-1599 ◽  
Author(s):  
Kejal Khatri ◽  
Vishnu Narayan Mishra
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Hölder Metric

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

2002 ◽  
Vol 33 (4) ◽  
pp. 365-370 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fourier Series ◽  
Series Representation ◽  
Triangular Matrix ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Matrix Means ◽  
The Matrix

In a recent paper Lal [1] obtained a theorem on the degree of approximation of the conjugate of a function belonging to the weighted $ W(L^p, \xi(t))$ class using a triangular matrix transform of the conjugate series of the Fourier series representation of the function. The matrix involved was assumed to have monotone increasing rows. We establish the same result by removing the monotonicity conditon.

scholarly journals Product Summability Transform of Conjugate Series of Fourier Series

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Kejal Khatri ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Increasing Function

A known theorem, Nigam (2010) dealing with the degree of approximation of conjugate of a signal belonging toLipξ(t)-class by(E,1)(C,1)product summability means of conjugate series of Fourier series has been generalized for the weightedW(Lr,ξ(t)),(r≥1),(t>0)-class, whereξ(t)is nonnegative and increasing function oft, byEn1Cn1~which is in more general form of Theorem 2 of Nigam and Sharma (2011).

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