The composition of solutions of the multidimensional translation equation

Under certain conditions, the general solution of the multidimensional translation equation was constructed locally in L. Berg 4] and globally in J. Aczél, L. Berg and Z. Moszner 2]. By composition of two of these solutions there arise new functional equations, which are solved here locally using generalized inverses, cf. A. Ben-Israel and T.N.E. Greville 5]. The results are illustrated by the linear case.