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Research articles

ScienceAsia 50 (2024):ID 2024048 1-7 |doi: 10.2306/scienceasia1513-1874.2024.048

An alternative functional equation related to the quadratic equation

Choodech Srisawat

ABSTRACT:     Given a rational number ? ?= 2, we establish a criterion for the existence of the general solution of an alternative quadratic functional equation of the form f (x y) + f (x y?1 ) = 2f (x) + 2f ( y) or f (x y) + f (x y?1 ) = ?f (x) + 2f ( y), where f is a mapping from an abelian group (G,?) to a uniquely divisible abelian group (H,+). We also find the general solution in the cases when G is a 6-divisible abelian group and G is a cyclic group.

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a Department of Mathematics and Statistics, Faculty of Science, Udon Thani Rajabhat University, Udon Thani 41000 Thailand

* Corresponding author, E-mail: ch.srisawat@gmail.com

Received 14 Aug 2023, Accepted 23 Mar 2024