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).

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 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 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.

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 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 Degree of approximation of conjugate of Lip $ \alpha$ class function by $ {K^\lambda}$-summability means of conjugate series of a Fourier series

2003 ◽  
Vol 34 (4) ◽  
pp. 387-394
Author(s):  
Shyam Lal ◽  
Gopal Krishna Singh
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Class Function

In this paper the degree of approximation of conjugate of a function belonging to Lip $ \alpha$ class by $ K^\lambda$-summability means of conjugate series of its Fourier series has been determined.

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