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

M. Misra¹, B. Majhi², B.P. Padhy³, P. Samanta⁴ and U.K. Misra^5,

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

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(L^p,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(L^p,ξ(t)) by product summability of the conjugate series of Fourier series associated with f has been established.

Keywords

degree of approximation, W(L^p,ξ(t)) class of function, (E,q) mean, mean, product mean, Fourier series, conjugate series, Lebesgue integral.

Copyright

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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).