On The Gibbs Phenomenon for \(|N,p_n,q_n|\)-Summability Method

Aditya Kumar Raghuvanshi

Abstract


In this paper we have proved a theorem on the Gibbs phenomenon for \(|N,p_n,q_n|\)-summability method which gives some new results and generalizes some previous known results.

Keywords


Approximation; Convergence; Fourier series; \((C,\alpha)\) summability and \(|N,p_n,q_n|\)-summability method

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References


D.J. Borwin, On product of sequences, J. of Lon. Moth. Soc. 33(1958).

H.P. Dikshit and A. Kumar, Absolute total effectiveness of $(N,p_n)$ means, I. Moth. Proc. Camb. Phil. Soc. (1975).

R.W. Hamming, Digital Filters, Printice-Hall, Englewood Cliffs, N.J. (1977).

E. Hille and J.D. Tamarkin, On the summability of Fourier series I, Trans. Amer. Math. Soc. 34 (1932).

K. Knoopp, Theory and application of infinite series, Blackie and Son Limited, London and Glasgow (1947).

S.N. Singh, On the Gibbs phenomenon for Nörlund method of summability, Carib J. Sci. Tech. 1 (2013).

Z. Zygmund, Trigonometric series, Camb. Uni. Press London (1968).




DOI: http://dx.doi.org/10.26713%2Fcma.v5i3.251

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