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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^*.

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* Corresponding author, E-mail: Paisan.N@chula.ac.th

Received 10 Nov 2014, Accepted 30 Jan 2015