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Multiplication of Strongly Summable Series

Published online by Cambridge University Press:  18 May 2009

A. V. Boyd
A. V. Boyd
Affiliation:
University of the Witwatersrand, Johannesburg
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Given a series we define , by the relations

The series is said to be summable (C, k), where k > - 1, to the sum s if

to be summable (C, - 1) to s if it converges to s and nan = o(l); to be absolutely summable (C, k), or summable | C, k, to s if it is summable (C, k) to s and

and to be strongly Cesàro summable to s with order k > 0 and index p or summable [C; k, p] to s, if

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 1 , December 1958 , pp. 29 - 33
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

1.Hyslop, J. M., Note on the strong summability of series, Proc. Glasgow Math. Assoc., 1 (1952), 16–20.CrossRefGoogle Scholar
2.Winn, C. E., On strong summability for any positive order, Math. Zeil., 37 (1933), 481–492.CrossRefGoogle Scholar