An alternative quadratic functional equation on 2-divisible groups
Paisan Nakmahachalasint
ABSTRACT: Let (G,⋅) be a 2-divisible group and let (G*,+) be a uniquely divisible abelian group. We show that the alternative quadratic functional equation f(xy−1)+f(xy)=±2(f(x)+f(y)) is equivalent to the quadratic functional equation f(xy−1)+f(xy)=2f(x)+2f(y) for the class of functions f:G→G*.