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A General Inclusion Theorem for l-l Nörlund Summability

Published online by Cambridge University Press:  20 November 2018

J. Defranza
J. Defranza*
Affiliation:
Department of Mathematical and Computer Sciences, Youngstown State University, Youngstown Ohio44555
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Abstract

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Nӧrlund methods of summability are studied as mappings from I1 into I1. Conditions are given for an arbitrary l-l method to include a Nӧrlund method. In particular necessary and sufficient conditions are given for a row finite l-l method to include a Nӧrlund mean.

Keywords

40D2540G05Inclusion TheoremI-l methodNörlund method
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 447 - 455
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Choudhary, B. and Vermes, P., Semi-Translative Summability Methods, Studia Scientiarum Mathematicarum Hungarica, 1 (1966), 403-410.Google Scholar
2. DeFranza, J., An Ordered Set of Nörlund Means, International Journal of Math, and Math. Sci., (To appear in Vol. 3 (1980)).Google Scholar
3. Fridy, J., Tauberian theorems via Block Dominated Matrices, Pacific Journal of Math., Vol. 81, 1 (1979), 81-91.Google Scholar
4. Hardy, G. H., Divergent Series, Oxford University Press, (1949).Google Scholar
5. Knopp, K., Infinite Sequences and Series, Dover Publications Inc., (1956).Google Scholar
6. Knopp, K. and Lorentz, G. G., Beiträge Zur Absoluten Limitierung, Arch. Math. 2 (1949), 10-16.Google Scholar
7. Powell, R. E. and Shah, S. M., Summability Theory and Applications, Van Nostrand Reinhold Co., (1972).Google Scholar