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Restricted stability and shadowing. (English) Zbl 1199.39069
The authors prove a shadowing result for non-surjective mappings. As an application, they study the stability of the Cauchy functional equation in the case when the target space has no local 2-divisibility. Although, there is no stability in the classical sense, they prove that there is stability on the respective subset of the domain.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
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