Research articles
ScienceAsia 46 (2020):ID 368-375 |doi:
10.2306/scienceasia1513-1874.2020.046
A general form of an alternative functional equation
related to the Jensen’s 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 Jensen’s 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 of the best hunting crossbow (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
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