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On approximately additive functions. (English) Zbl 0820.39013

The author continues his studies concerning possible generalizations of the concept of invariant mean.
In the first part of the paper a theorem is proved which guarantees the existence of a left-invariant mean on a space of functions, larger than the space of bounded functions, from a left-amenable semigroup into a locally convex topological Hausdorff space.
In the second part the previous result is applied to get a stability theorem (in the sense of Hyers-Ulam) for the Cauchy functional equation, which generalizes many of the known results.
Reviewer: G.L.Forti (Milano)

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
43A07 Means on groups, semigroups, etc.; amenable groups
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