On a Functional Equation Related to the Determinant of Symmetric Two-By-Two Matrices
DOI:
https://doi.org/10.5644/SJM.03.1.07Keywords:
Determinant, functional equation, logarithmic function, multiplicative functionAbstract
The present work aims to find the solutions $f,g,h, \ell , m : \mathbb{R}^2 \to \mathbb{R}$ of the functional equation $f( ux - vy , \, uy - vx ) = g(x, y ) + h(u, v) + \ell (x , y ) \, m(u , v)$ for all $x, y, u, v \in \mathbb{R}$ without any regularity assumptions on the unknown functions. This equation is a generalization of a functional equation which arises from the characterization of the determinant of symmetric matrices.
2000 Mathematics Subject Classification. Primary 39B22
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