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Zbl 0619.39012
Forti, G.L.
The stability of homomorphisms and amenability, with applications to functional equations. (English)
[J] Abh. Math. Semin. Univ. Hamb. 57, 215-226 (1987). ISSN 0025-5858; ISSN 1865-8784/e

Following a well known result of {\it D. H. Hyers} [Proc. Natl. Acad. Sci. USA 27, 222-224 (1941; Zbl 0061.264)], the concept of stability for the homomorphisms from a group into a Banach space is defined. Some consequences of the stability are proved and then the connections between the stability of the homomorphisms and the amenability of the group are investigated. The results obtained are used for solving some alternative Cauchy functional equations.

MSC 2000:: *39B52 Functional equations for functions with more general domains
39B99 Functional equations
43A07 Means on groups, etc.

Keywords: stability; amenability; alternative functional equation; Banach space; Cauchy functional equations

Citations: Zbl 0061.264

Cited in: Zbl 1072.39027 Zbl 0757.47033

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