|
Stability of additive mappings on large subsets
Author(s):
Félix
Cabello
Sánchez
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1071-1077.
MSC (2000):
Primary 39B82, 39B55
Posted:
September 24, 1999
MathSciNet review:
1646206
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study mappings from a group into a Banach space which are ``nearly additive'' on large subsets.
References:
- 1.
- F. Cabello Sánchez, Some remarks stemming from Ulam's problem about nearly additive mappings, Aequationes Math. 56 (1998), 233-242. CMP 98:17
- 2.
- F. Cabello Sánchez and J. M. F. Castillo, Banach space techniques underpinning a theory for nearly additive mappings, Universidad de Extremadura, preprint 1998.
- 3.
- G. L. Forti, The stability of homomorphisms and amenability, with applications to functional equations, Abh. Math. Sem. Univ. Hamburg 57 (1987), 215-226. MR 89b:39013
- 4.
- G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), 143-190. MR 96i:39033
- 5.
- Z. Gajda, On stability of additive mappings, Internat. J. Math. Sci. 14 (1991), 431-434. MR 92e:39029
- 6.
- Z. Gajda and Z. Kominek, On separation theorems for subadditive and superadditive functionals, Studia Math. 100 (1991), 25-38. MR 93h:39003
- 7.
- R. Ger, On functional inequalities stemming from stability questions, General Inequalities 6 (W. Walter, Ed.), International Series in Numerical Mathematics 103 (227-240), Birkhäuser, 1992. MR 94b:39042
- 8.
- F. P. Greenleaf, Invariant means on topological groups, Van Nostrand Math. Studies 16, New York, 1969. MR 40:4776
- 9.
- D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153. MR 93i:39007
- 10.
- D. H. Hyers, G. Isac and Th. M. Rassias, On the asymptoticity aspect of Hyers-Ulam stability of mappings, Proc. Amer. Math. Soc. 126 (1998), 425-430. MR 98d:39004
- 11.
- B. E. Johnson, Approximately multiplicative maps between Banach algebras, J. London Math. Soc. 37 (1988), 294-316. MR 89h:46072
- 12.
- Å. Lima and D. Yost, Absolutely Chebyshev subspaces, Proc. Cent. Math. Anal. Austra. Nat. Univ. 20 (1988), 116-127. MR 90h:46030
- 13.
- Th. M. Rassias and P. \v{S}emrl, On the behaviour of mappings which do not satisfy the Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993. MR 92g:47101
- 14.
- M. Ribe, Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc. 73 (1979), 351-355. MR 81a:46010
- 15.
- P. \v{S}emrl, The stability of approximately additive functions, Stability of mappings of Hyers-Ulam type (edited by Th. M. Rassias and J. Tabor), Hadronic Press, Florida (1994), 135-140. MR 95i:39029
- 16.
- S. M. Ulam, An Anecdotal History of the Scottish Book (The Scottish Book, edited by R. D. Mauldin), Birkhäuser, 1981.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
39B82, 39B55
Retrieve articles in all Journals with
MSC (2000):
39B82, 39B55
Additional Information:
Félix
Cabello
Sánchez
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071-Badajoz, Spain
Email:
fcabello@unex.es
DOI:
10.1090/S0002-9939-99-05218-1
PII:
S 0002-9939(99)05218-1
Keywords:
Cauchy functional equation,
stability,
amenable group
Received by editor(s):
May 28, 1998
Posted:
September 24, 1999
Additional Notes:
This research was supported in part by DGICYT project PB97-0377 and HI project 1997-0016.
Communicated by:
Dale Alspach
Copyright of article:
Copyright
2000,
American Mathematical Society
|
