On a Functional Equation Related to the Determinant of Symmetric Two-By-Two Matrices - Houston, Kelly B.; Sahoo, P. K. (Sarajevo Journal of Mathematics, 2024)
The present work aims to find the solutions f,g,h, , m : R^2 → R of the functional equation f( ux - vy , uy - vx ) = g(x, y ) + h(u, v) + (x , y ) m(u , v) for all x, y, u, v 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