American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2014, 2(5), 352-356
DOI: 10.12691/ajams-2-5-9
Open AccessArticle

Approximation of Conjugate Series of the Fourier Series of a Function of Class W(Lp,ξ(t)) by Product Means

M. Misra1, B. Majhi2, B.P. Padhy3, P. Samanta4 and U.K. Misra5,

1Department of Mathematics Binayak Acharya College, Berhampur, Odisha, India

2Department of Mathematics GIET, Gunupur, Odisha, India

3Department of Mathematics Roland Institute of Technology, Golanthara, Odisha, India

4Department of Mathematics Berhampur University, Berhampur, Odisha, India

5Department of Mathematics National Institute of Science and Technology Pallur Hills, Golanthara, Odisha, India

Pub. Date: October 29, 2014

Cite this paper:
M. Misra, B. Majhi, B.P. Padhy, P. Samanta and U.K. Misra. Approximation of Conjugate Series of the Fourier Series of a Function of Class W(Lp,ξ(t)) by Product Means. American Journal of Applied Mathematics and Statistics. 2014; 2(5):352-356. doi: 10.12691/ajams-2-5-9

Abstract

In this paper a theorem on degree of approximation of a function f∈W(Lp,ξ(t)) by product summability of the conjugate series of Fourier series associated with f has been established.

Keywords:
degree of approximation W(Lpξ(t)) class of function (Eq) mean mean product mean Fourier series conjugate series Lebesgue integral.

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References:

[1]  G.H. Hardy, Divergent Series (First Edition), Oxford University Press, (1970).
 
[2]  U.K. Misra, M. Misra, B.P. Padhy and S.K. Buxi, “On degree of approximation by product means of conjugate series of Fourier series”, International Jour. of Math. Scie. And Engg. Appls. ISSN 0973-9424, Vol 6 No. 1 (Jan. 2012), pp 363-370
 
[3]  Misra U.K.,Paikray, S.K., Jati, R.K, and Sahoo, N.C.: “On degree of Approximation by product means of conjugate series of Fourier series”, Bulletin of Society for Mathematical Services and Standards ISSN 2277-8020, Vol. 1 No. 4 (2012), pp 12-20.
 
[4]  U.K. Misra, M. Misra, B.P. Padhy and D.Bisoyi, “On Degree of Approximation of conjugate series of a Fourier series by product summability" Malaya Journal of Mathematik (ISSN: 2319-3786, Malayesia), Vol. 1 Issue 1 (2013), pp 37-42.
 
[5]  E.C. Titchmarch, The Theory of Functions, Oxford University Press, (1939).
 
[6]  A. Zygmund, Trigonometric Series (Second Edition) (Vol. I), Cambridge University Press, Cambridge, (1959).