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A Tauberian theorem concerning weighted means and power series

Published online by Cambridge University Press:  24 October 2008

David Borwein  and
Amram Meir
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ont. N6A 5B7, Canada
Amram Meir
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alta. T6G 2G1, Canada
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Extract

Suppose throughout that {pn} is a sequence of non-negative numbers with p0 > 0, that

and that

Let {sn} be a sequence of real numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 283 - 286
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Borwein, D.. Tauberian conditions for the equivalence of weighted mean and power series methods of summability. Canad. Math. Bull. 24 (1981), 309–316.CrossRefGoogle Scholar
[2]Feller, W.. An Introduction to Probability Theory and Its Applications, 2nd ed., vol. 2 (John Wiley, 1971).Google Scholar
[3]Hardy, G. H. and Wright, E. M.. An Introduction to the Theory of Numbers, 4th ed. (Oxford University Press, 1960).Google Scholar
[4]Ishiguro, K.. A Tauberian theorem for (J, pn) summability. Proc. Japan Acad. 40 (1964), 807–812.Google Scholar