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On bounded sequences satisfying a linear inequality

Published online by Cambridge University Press:  20 January 2009

Dennis C. Russell
Dennis C. Russell
Affiliation:
York University, Downsview, Ont., M3J 1P3, Canada
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In a recent paper, E. T. Copson (2) proves the following result:

Theorem C.Letki >0 (i = 1, …, m), k1 +…+ km = 1, and the real sequence (an) satisfy the inequality

If (an) is bounded, then it must be convergent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 1 , March 1974 , pp. 11 - 16
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Borwein, D., Convergence criteria for bounded sequences, Proc. Edinburgh Math. Soc. (2) 18 (1972), 99–103.CrossRefGoogle Scholar
(2) Copson, E. T., On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. (2) 17 (1970), 159–164.CrossRefGoogle Scholar
(3) Peyerimhoff, A., Lectures on Summability (Lecture Notes in Mathematics, vol. 107, Springer, 1969).CrossRefGoogle Scholar
(4) Rado, R., Some elementary Tauberian theorems (I), Quart. J. Math. Oxford Ser. 9 (1938), 274–282.CrossRefGoogle Scholar