Stability of a functional equation related to distance measure. II. (English) Zbl 1203.39018
Summary: The present work continues the study of the stability of the functional equations of the type $f (pr, qs) + f (ps, qr) = f (p, q) f (r, s)$, namely, (i) $f (pr, qs)+f (ps, qr) = g(p, q) g(r, s)$, and (ii) $f (pr, qs)+f (ps, qr) = g(p, q) h(r, s)$ for all $p, q, r, s \in G$, where $G$ is an abelian group. These functional equations arise in the characterization of symmetrically compositive sum form distance measures.
|39B82||Stability, separation, extension, and related topics|
|39B52||Functional equations for functions with more general domains and/or ranges|