ScienceAsia 41(2015): 136-140 |doi:
An alternative quadratic functional equation on 2-divisible groups
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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|Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330 Thailand
* Corresponding author, E-mail: Paisan.N@chula.ac.th
Received 10 Nov 2014, Accepted 30 Jan 2015