On degree of approximation of conjugate series of a Fourier series by product summability

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DOI:

https://doi.org/10.26637/mjm102/005

Abstract

In this paper a theorem on degree of approximation of a function f∈Lip(α,r)  by product summability (E,q)(ˉN,pn) of conjugate series of Fourier series associated with f has been proved.

Keywords:

Degree of Approximation, Fourier series, conjugate of the Fourier series, Lebesgue integral, Lip(α,r) class of function, (E,q) mean, (ˉN,pn) mean

Mathematics Subject Classification:

42B05, 42B08
  • Mahendra Misra P. G. Department of Mathematics, N. C. College(Autonomous), Jajpur, Odisha, India.
  • B. P. Padhy Department of Mathematics, Roland Institute of Technology, Golanthara-761008, Odisha, India.
  • Dattaram Bisoyi Department of Mathematics, L. N. Mahavidyalaya, Kodala, Ganjam, Odisha, India.
  • U. K. Misra Department of Mathematics, National Institute of Science and Technology, Palur Hills, Golanthara-761008, Odisha, India.
  • Pages: 37-42
  • Date Published: 01-04-2013
  • Vol. 1 No. 02 (2013): Malaya Journal of Matematik (MJM)

G.H. Hardy, Divergent Series, First Edition, Oxford University Press, 70,(19).

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 Journal of Math. Science and Engineering Applications, 6(1)(2012), 363-370.

S.K. Paikray, U.K. Misra, R.K. Jati, and N.C. Sahoo, On degree of Approximation of Fourier Series by Product Means, Bull. of Society for Mathematical Services and Standards, 1(4)(2012), 12-20. DOI: https://doi.org/10.18052/www.scipress.com/BSMaSS.4.5

Titchmarch, E.C. , The Theory of Functions, Oxford University Press, 1939, 402-403.

Zygmund, A. , Trigonometric Series, Second Edition, Cambridge University Press, Cambridge, 1959.

  • NA

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Published

01-04-2013

How to Cite

Mahendra Misra, B. P. Padhy, Dattaram Bisoyi, and U. K. Misra. “On Degree of Approximation of Conjugate Series of a Fourier Series by Product Summability”. Malaya Journal of Matematik, vol. 1, no. 02, Apr. 2013, pp. 37-42, doi:10.26637/mjm102/005.

Issue

Vol. 1 No. 02 (2013): Malaya Journal of Matematik (MJM)

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