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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some relations between Nörlund
and Abel summability


Author: J. R. Nurcombe
Journal: Proc. Amer. Math. Soc. 125 (1997), 183-187
MSC (1991): Primary 40E05, 40F05, 40G05
MathSciNet review: 1346982
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Abstract: The definition of generalised Abel summability is extended to positive orders and a definition of strong generalised Abel summability is introduced. A result of Jurkat and Peyerimhoff concerning the implication between Nörlund and generalised Abel summabilities is extended to positive integral order. Analogous results for the corresponding strong methods are also given.


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Additional Information

J. R. Nurcombe
Affiliation: South Birmingham College, Cole Bank Road, Hall Green, Birmingham B28 8ES, England

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03552-1
PII: S 0002-9939(97)03552-1
Keywords: Summability, strong, N\"orlund, Abel, convergence, sequence
Received by editor(s): March 9, 1995
Received by editor(s) in revised form: July 13, 1995
Communicated by: Theodore Gamelin
Article copyright: © Copyright 1997 American Mathematical Society