A sine type functional equation on a topological group

Abstract

In [13] H. Stetkaer obtained the complex valued solutions of the functional equation f (xyz 0)f (xy −1 z 0) = f (x) 2 − f (y) 2 , x,y ∈ G, where G is a topological group and z 0 ∈ Z(G) (the center of G). Our main goal is first to remove this restriction and second, when G is 2divisible and abelian, we will investigate the superstability of the above functional equation.