Abstract
Let R be a ring, \({\mathbb{F}}\) be a field and \({K \subset \mathbb{R}}\) an integral domain. In this paper we investigate general solutions \({f : K^2\to \mathbb{R}^+}\) of the functional equations
for all \({x, y\in K}\), and general solutions \({f:R^2\to \mathbb{R}^+}\) of the functional equations
for all \({x, y\in R}\). The above functional equations arise from number theory and are connected with the characterizations of the determinant and permanent of two-by-two matrices.
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Chung, J., Chang, J. Multiplicative type functional equations in a ring. Aequat. Math. 90, 367–379 (2016). https://doi.org/10.1007/s00010-015-0340-8
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DOI: https://doi.org/10.1007/s00010-015-0340-8