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Convergence criteria for bounded sequences

Published online by Cambridge University Press:  20 January 2009

D. Borwein
D. Borwein
Affiliation:
University of Western Ontario, London, Canada
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Let {Kn} be a sequence of complex numbers, let

and let

Let D be the open unit disc {z: |z| <1}, let be its closure and let .

The primary object of this paper is to prove the two theorems stated below, the first of which generalises a result of Copson (1).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 2 , December 1972 , pp. 99 - 103
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Copson, E. T., On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. 17 (1970), 159–164.CrossRefGoogle Scholar
(2) Zygmund, A., Trigonometric Series, Vol. 1 (Cambridge, 1959).Google Scholar