On Tauberian Theorems for Some Standard Methods of Summability

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Authors

  • C. T. Rajagopal
     The Anchorage, Agaram Road, Madras-59 ,IN

Abstract

On summabilities (Aα) and (Ax). P. A. Jeyarajan has proved ([3], Theorem 4) the Tauberian theorem for generalized Abel summability (Aα) appearing as Theorem 1(Aα) in this note.

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Published

1975-12-01

How to Cite

Rajagopal, C. T. (1975). On Tauberian Theorems for Some Standard Methods of Summability. The Journal of the Indian Mathematical Society, 39(1-4), 69–82. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16637

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 C. T. Rajagopal

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

G.H. HARDY. Divergent Series (Oxford, 1949).

A. JAKIMOWSKI AND M.R. PARAMESWARAN. Generalized Tauberian theorems for summability-(-4), Quart. J. Math. Oxford (2) 9(1958), 290-298.

P.A. JEYARAJAN. A Tauberian theorem for the generalized Abel method of summabitity-I, J. Indian Math. Soc. New Ser. 36(1972), 279-289.

W.B. PENNINGTON. On Ingham summability and summability by Lambert series, Proc. Cambridge Philos. Soc. 51 (1955), 65-80.

H.R. PITT. Tauberian Theorems (Tata Institute of Fundamental Research Monographs No. 2, Bombay, 1958).

C.T. RAIAGOPAL. A note on "positive" Tauberian theorems, J. London Math.Soc. 25 (1950), 315-327.

A note on the oscillation of Riesz, Euler and Ingham means, Quart. J. Math. Oxford (2) 7 (1956), 64-75.

On the Riemann-Ceskro summability of series and integrals. Tbhoku Math. J. (2) 9 (1957), 247-263.

Tauberian theorems on oscillation for the (®,X) method, Publ. Ramanujan Inst. 1 (1969), 246-267.

M.S. RANGACHARI AND Y. SITARAMAN. Tauberian theorems for logarithmic summability (Z,), Tbhoku Math. J. (2) (16) (1964), 257-269.