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On Integral Abel-Type and Logarithmic Methods of Summability

Published online by Cambridge University Press:  20 November 2018

E. C. Heagy  and
B. L. R. Shawyer
E. C. Heagy
Affiliation:
Scarborough College, University of Toronto, 1265 Military Trail, West Hill, OntarioCanadaMIC 1A4.
B. L. R. Shawyer
Affiliation:
Department of Mathematics, University of Western Ontario, LondonOntarioCanadaN6A 5B9.
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In this paper, we define an integral logarithmic method of summability, extending the integral Abel-type methods defined by Jakimovski [6]. We examine the behaviour of the product of this method with integral Hausdorff methods. A full scale of strict inclusions for integral Abel-type methods is obtained and the integral logarithmic method is placed in this scale.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 207 - 213
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Borwein, D., A logarithmic method of summability, J. London Math. Soc., 33 (1958), 212-220.Google Scholar
2. Borwein, D., On a scale of Abel-type summability methods, Proc. Cambridge Philos. Soc., 53 (1957), 318-322.Google Scholar
3. Borwein, D., On methods of summability based on integral functions, II, Proc. Cambridge Philos. Soc., 56 (1960), 125-131.Google Scholar
4. Borwein, D., Theorems on some methods of summability, Quart. J. Math. (Oxford Ser.), 9 (1958), 310-316.Google Scholar
5. Hardy, G. H., Divergent Series, Oxford, Oxford, 1949.Google Scholar
6. Jakimovski, A. (A. Amir), Some remarks on Tauberian theorems, Quart. J. Math. (Oxford Ser.), 9 (1958), 114-131.Google Scholar
7. Rogosinski, W. W., On Hausdorff's methods of summability, Proc Cambridge Philos. Soc., 38 (1942), 166-192.Google Scholar
8. Rogosinski, W. W., On Hausdorff's methods of summability, II, Proc. Cambridge Philos. Soc., 38 (1942), 344-363.Google Scholar
9. Watson, B. B., Tauberian theorems on a scale of Abel-type summability methods, Ph.D. Thesis, University of Western Ontario, 1974.Google Scholar
10. Widder, D. V., The Laplace Transform, Princeton University Press, Princeton, 1946.Google Scholar