Stability of a functional equation related to distance measures - II

Abstract

‎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 sumform distance measures‎.