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Research articles

ScienceAsia 41(2015): 280-288 |doi: 10.2306/scienceasia1513-1874.2015.41.280


An alternative functional equation of Jensen type on groups


Choodech˙Srisawat, Nataphan˙Kitisin*, Paisan˙Nakmahachalasint

 
ABSTRACT:     Given an integer λ≠2, we establish the general solution of an alternative functional equation of Jensen type on certain groups. First, we give a criterion for the existence of the general solution for the functional equation f(xy−1)−2f(x)+f(xy)=0 or f(xy−1)−λf(x)+f(xy)=0, where f is a mapping from a group (G,⋅) to a uniquely divisible abelian group (H,+). Then we show that, for λ∉{0,−1,−2}, the above alternative functional equation is equivalent to the classical Jensen's functional equation. We also find the general solution in the case when G is a cyclic group and λ≠2 is an integer.

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Department˙of˙Mathematics˙and˙Computer˙Science, Faculty˙of˙Science, Chulalongkorn˙University, Bangkok˙10330˙Thailand

* Corresponding author, E-mail: nataphan.k@chula.ac.th

Received 19 Feb 2015, Accepted 20 Aug 2015