On a Theorem of Sunouchi

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Authors

  • Department of Mathematics, Sambalpur University, Burla, Sambalpur, Orissa ,IN

Abstract

This result is best possible in the sense that δ cannot be dropped.

The special case of this theorem in which α is an integer has been generalised as follows by introducing a general sequence of factors:

Theorem S'. [7], [11]. Let λn > 0 and non-decreasing and let α be a non-negative integer and let

Σ |σαn-σαn-1| = O(λm).

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Published

1974-12-01

How to Cite

Das, G. (1974). On a Theorem of Sunouchi. The Journal of the Indian Mathematical Society, 38(1-4), 155–174. Retrieved from http://www.informaticsjournals.com/index.php/jims/article/view/16689

 

References

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L. S. BOSANQUET AND G. DAS : Absolute summability factors for Nbrlund means (to appear)

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G. DAS: Tauberian theorems for absolute Norlund summability Proc. Lond. Math. Soc. (3), 19(1969) 357-384.

G. DAS AND R. N. MOHAPATRA: The non-absolute Norlund summability of Fourier series Pacific. Jour. Math. 51 (1974) 49-55.

G. D. DIKSHIT: On the absolute summability factors of infinite series, Proc. Nat. Inst. Sci. India. Part A, 3(1959) 191-200.

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K. S. K. IYENGAR: A Tauberian theorem and its application to convergence of Fourier series, Proc. Indian Acad. Sci. Sec. A, 18(1943) 81-87.

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V. P. SRIVASTAVA : Extension of a theorem of Sunouchi, Proc. Camb. Phil. Soc, 65 (1969) 489–494.

G. SUNOUCHI: On the absolute summability factors, Kodai Math, Seminar Report (1954).

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