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Some relations between Nörlund and Abel summability
Author(s):
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.
References:
- 1.
- D. Borwein, On a scale of Abel type summability methods, Proceedings Cambridge Phil. Soc. 53 (1957), 318-322. MR 19:134f
- 2.
- D. Borwein and F. P. Cass, Strong Nörlund summability, Math. Zeitschrift 103 (1968), 94-111. MR 37:643
- 3.
- T. M. Flett, Some remarks on strong summability, Quart. Journ. of Math. (Oxford) 10 (1959) 115-139. MR 21:6491
- 4.
- G. H. Hardy, Divergent Series, (Oxford 1949). MR 11:25a
- 5.
- W. Jurkat and A. Peyerimhoff, The consistency of Nörlund and Hausdorff methods, Annals of Math. 62 (1955), 498-503. MR 17:359a
- 6.
- B. P. Mishra, Strong summability of infinite series on a scale of Abel type summability methods, Proceedings Cambridge Phil. Soc. 63 (1967), 119-127. MR 34:3156
- 7.
- J. R. Nurcombe, On absolute Nörlund and Abel summability, Journ. Indian Math. Soc. 53 (1988), 217-226. MR 90k:40008
- 8.
- M. A. Sarigöl, A relation between Nörlund and Abel summabilities, Proceedings American Math. Soc. 122 (1994), 223-225. MR 95d:40015
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Additional Information:
J.
R.
Nurcombe
Affiliation:
South Birmingham College, Cole Bank Road, Hall Green, Birmingham B28 8ES, England
DOI:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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