A functional equation of Ih-Ching Hsu

Abstract

A recent note of Ih-Ching Hsu poses an unsolved problem, to wit, the general solution of the functional equation g(x1, x2) + g(φ1(x1), φ2(x2)) = g(x1, φ2(x2)) + g(φ1(x1),x2), where the φi are given functions. This short paper obtains the general solution. It gives conditions which imply that any continuous solution has form g1(x1) + g2(x2). © 1989 Birkhäuser Verlag.