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On stability of some functional equations and topology of their target spaces. (English) Zbl 1292.39027
Summary: Some remarks about the coherence of the stability of several functional equations with topology of their target spaces are given. The equations in question are: homogeneity (first of all) and quadratic ones, as well as those of Drygas, Jensen and Schröder. Moreover, we prove, by method different than those used in earlier papers, the superstability of the following equations: Dhombres’, Lobachevski’s and Mikusiński’s and those of cosine, sine and of homomorphisms.

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges