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Volume 46 Number 2 Volume 46 Number 3 Volume 46 Number 4

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Research articles

ScienceAsia 46 (2020): 368-375 |doi: 10.2306/scienceasia1513-1874.2020.046


A general form of an alternative functional equation related to the Jensenís functional equation


Nataphan Kitisina,*, Choodech Srisawatb

 
ABSTRACT:     Given integers α, β, γ such that (α, β, γ) ≠ (k, −2k, k) for all k ∈ , we will establish a criterion for the existence of the general solution of the alternative Jensenís functional equation of the form ƒ (x y−1)−2ƒ (x)+ ƒ (x y) = 0 or α ƒ (x y−1)+β ƒ (x)+γ ƒ (x y) = 0, where ƒ is a mapping from a group (G, ·) to a uniquely divisible abelian group (H, +). We also find the general solution in the case when G is a cyclic group.

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a Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330 Thailand
b Department of Mathematics, Faculty of Science, Udon Thani Rajabhat University, Udon Thani 41000 Thailand

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

Received 17 Feb 2020, Accepted 11 Jun 2020