Stability of the equation of homomorphism and completeness of the underlying space

Abstract

We prove that all assumptions of a Theorem of Forti and Schwaiger (cf. [G. L. Forti, J. Schwaiger, Stability of homomorphisms and completeness, C. R. Math. Rep. Acad. Sci. Canada 11 (1989), 215–220]) on the coherence of stability of the equation of homomorphism with the completeness of the space of values of all these homomorphisms, are essential. We give some generalizations of this theorem and certain examples of applications.

Keywords

• functional equation
• stability of equations of homomorphisms
• superstability
• complete vector spaces