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The stability of homomorphisms and amenability, with applications to functional equations. (English) Zbl 0619.39012
Following a well known result of 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:
39B52 Functional equations for functions with more general domains and/or ranges
39B99 Functional equations and inequalities
43A07 Means on groups, semigroups, etc.; amenable groups
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