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On a conjecture on Riemann summability (R, k)

Published online by Cambridge University Press:  24 October 2008

B. Kwee
B. Kwee
Affiliation:
Department of Mathematics, University of Malaya, 59100 Kuala Lumpur, Malaysia
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Extract

The series is said to be summable (R, k) to s, where k is a positive integer, if

converges for all values of h in some neighbourhood of the origin and if its sum tends to s as h → 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 277 - 281
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Hardy, G. H. and Wright, E. M.. An Introduction to the Theory of Numbers (Oxford University Press, 1965).Google Scholar
[2]Kwee, B.. The relation between Abel and Riemann summability. J. London Math. Soc. 39 (1964), 5–11.CrossRefGoogle Scholar
[3]Verblunsky, S.. On the theory of trigonometric series (VI). Proc. London Math. Soc. (2) 38 (1935), 284–326.CrossRefGoogle Scholar