Stability of additive mappings on large subsets
HTML articles powered by AMS MathViewer
- by Félix Cabello Sánchez PDF
- Proc. Amer. Math. Soc. 128 (2000), 1071-1077 Request permission
Abstract:
We study mappings from a group into a Banach space which are “nearly additive” on large subsets.References
- F. Cabello Sánchez, Some remarks stemming from Ulam’s problem about nearly additive mappings, Aequationes Math. 56 (1998), 233–242.
- F. Cabello Sánchez and J. M. F. Castillo, Banach space techniques underpinning a theory for nearly additive mappings, Universidad de Extremadura, preprint 1998.
- G. L. Forti, The stability of homomorphisms and amenability, with applications to functional equations, Abh. Math. Sem. Univ. Hamburg 57 (1987), 215–226. MR 927176, DOI 10.1007/BF02941612
- Gian Luigi Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143–190. MR 1336866, DOI 10.1007/BF01831117
- Zbigniew Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431–434. MR 1110036, DOI 10.1155/S016117129100056X
- Zbigniew Gajda and Zygfryd Kominek, On separation theorems for subadditive and superadditive functionals, Studia Math. 100 (1991), no. 1, 25–38. MR 1130135, DOI 10.4064/sm-100-1-25-38
- Roman Ger, On functional inequalities stemming from stability questions, General inequalities, 6 (Oberwolfach, 1990) Internat. Ser. Numer. Math., vol. 103, Birkhäuser, Basel, 1992, pp. 227–240. MR 1213010, DOI 10.1007/978-3-0348-7565-3_{2}0
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- Donald H. Hyers and Themistocles M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125–153. MR 1181264, DOI 10.1007/BF01830975
- 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), no. 2, 425–430. MR 1415589, DOI 10.1090/S0002-9939-98-04060-X
- B. E. Johnson, Approximately multiplicative maps between Banach algebras, J. London Math. Soc. (2) 37 (1988), no. 2, 294–316. MR 928525, DOI 10.1112/jlms/s2-37.2.294
- Åsvald Lima and David Yost, Absolutely Chebyshev subspaces, Workshop/Miniconference on Functional Analysis and Optimization (Canberra, 1988) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 20, Austral. Nat. Univ., Canberra, 1988, pp. 116–127. MR 1009599
- Themistocles M. Rassias and Peter emrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), no. 4, 989–993. MR 1059634, DOI 10.1090/S0002-9939-1992-1059634-1
- M. Ribe, Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc. 73 (1979), no. 3, 351–355. MR 518518, DOI 10.1090/S0002-9939-1979-0518518-9
- Peter emrl, The stability of approximately additive functions, Stability of mappings of Hyers-Ulam type, Hadronic Press Collect. Orig. Artic., Hadronic Press, Palm Harbor, FL, 1994, pp. 135–140. MR 1304277
- S. M. Ulam, An Anecdotal History of the Scottish Book (The Scottish Book, edited by R. D. Mauldin), Birkhäuser, 1981.
Additional Information
- Félix Cabello Sánchez
- Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071-Badajoz, Spain
- Email: fcabello@unex.es
- Received by editor(s): May 28, 1998
- Published electronically: 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 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1071-1077
- MSC (2000): Primary 39B82, 39B55
- DOI: https://doi.org/10.1090/S0002-9939-99-05218-1
- MathSciNet review: 1646206