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Strong summability of infinite series on a scale of Abel type summability methods

Published online by Cambridge University Press:  24 October 2008

Babban Prasad Mishra
Babban Prasad Mishra
Affiliation:
The University, Gorakhpur, India
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Extract

Introduction. In a recent paper, Borwein(1) constructed a new method of summability which would read: Let

and let {sn} be any sequence of numbers. If, for λ > − 1,

is convergent for all x in the open interval (0,1) and tends to a finite limit s as x → 1 in (0,1), we say that the sequence {sn} is Aλ convergent to s and write sn → s(Aλ). The A0 method is the ordinary Abel method.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 119 - 127
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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