On degree of approximation of conjugate series of a Fourier series by product summability
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DOI:
https://doi.org/10.26637/mjm102/005Abstract
In this paper a theorem on degree of approximation of a function \(f \in \operatorname{Lip}(\alpha, r)\) by product summability \((E, q)\left(\bar{N}, p_n\right)\) 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, \(\operatorname{Lip}(\alpha, r)\) class of function, \((E, q)\) mean, \(\left(\bar{N}, p_n\right)\) meanMathematics Subject Classification:
42B05, 42B08- 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.
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