Stability of additive mappings on large subsets

Proceedings of the American Mathematical Society

Volumn 128, Issue 4, 2000, Pages 1071-1077

  Sánchez, Félix Cabello ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

Amenable group; Cauchy functional equation; Stability

Indexed keywords

EID: 33646839984     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-05218-1     Document Type: Article

References (16)

1. [I] F. Cabello Sánchez, Some remarks stemming from Utam'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 92c: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 931:39007
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 08d: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. Semrl, On the behaviour of mappings which do not satisfy the HyersUlam 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. Šemrl, The stability of approximately additive functions, Stability of mappings of HyersUlam 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.