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Zbl 1203.39018
Kim, G.H.; Sahoo, P.K.
Stability of a functional equation related to distance measure. II.
(English)
[J] Ann. Funct. Anal. AFA 1, No. 1, 26-35, electronic only (2010). ISSN 2008-8752/e

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.
MSC 2000:
*39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains

Keywords: distance measure; multiplicative function; sum form distance measure; stability of functional equation; abelian group

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