A Functional Equation with Biadditive Functions

Abstract

Abstract Let S, H, X be groups. For two given biadditive functions A : S2 → X, B : H2 → X and for two unknown mappings T : S → H, g : S → S we will study the functional equation B(T (x), T (y)) = A(x, g(y)), x, y ∈ S, which is a generalization of the orthogonality equation in Hilbert spaces.