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A Note on Convergence Factors

Published online by Cambridge University Press:  20 January 2009

C. E. Walsh
C. E. Walsh
Affiliation:
Trinity College, Dublin.
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Suppose that un ≥ un+1 > 0, for n = 1, 2, … and that e1, e2, … are factors which make convergent.

Let where all the a's are positive, diverges, and Define En by the equation

For the case where an = 1 it has been shewn by Fuchs1 and Karamata1 that, under various conditions, En = 0(1) The object of this note is to extend some of their results.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 3 , July 1956 , pp. 154 - 156
Copyright
Copyright © Edinburgh Mathematical Society 1956

References

1 Fuchs, W. H. J., Proc. Edinburgh Math. Soc. (2), 7 (1942), 27–30;CrossRefGoogle ScholarKaramata, J.Journal London Math. Soc., 21 (1946), 162–166.CrossRefGoogle Scholar