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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.

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)