Badora, Roman On approximately additive functions. (English) Zbl 0820.39013 Pr. Nauk. Uniw. Śląsk. Katowicach 1444, Ann. Math. Silesianae 8, 111-126 (1994). 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) Cited in 2 Documents MSC: 39B52 Functional equations for functions with more general domains and/or ranges 43A07 Means on groups, semigroups, etc.; amenable groups Keywords:approximately additive functions; Hyers-Ulam theorem; invariant mean; left-amenable semigroup; locally convex topological Hausdorff space; stability; Cauchy functional equation PDFBibTeX XMLCite \textit{R. Badora}, Pr. Nauk. Uniw. Śląsk. Katowicach, Ann. Math. Silesianae 1444(8), 111--126 (1994; Zbl 0820.39013)