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Research articles

ScienceAsia 41(2015): 136-140 |doi: 10.2306/scienceasia1513-1874.2015.41.136


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:GG*.

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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