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A generalization of summability-(Z, p) of Silverman and Szász

Published online by Cambridge University Press:  20 January 2009

David L. Sherry
David L. Sherry
Affiliation:
University of West Florida
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A sequence x = {si} has been defined to be summable-(Z, p) to s if

Where p is a positive integer and

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 53 - 57
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Borwein, D., Nörlund methods of summability associated with polynomials, Proc. Edinburgh Math. Soc. (2) 12(1959), 7–15.CrossRefGoogle Scholar
(2) Borwein, D. and Boyd, A. V., Binary and ternary transformations of sequences, Proc. Edinburgh Math. Soc. (2) 11 (1959), 175–181.CrossRefGoogle Scholar
(3) Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
(4) Hill, J. D. and Sledd, W. T., Summability-(Z, p) and sequences of periodic type, Canad. J. Math. 16 (1964), 741–754.CrossRefGoogle Scholar
Silverman, L. L. and Szász, O., On a class of Nörlund matrices, Ann. of Math. (2) 45 (1944), 347–357.CrossRefGoogle Scholar