General solution of some functional equations related to the determinant of some symmetric matrices

• Autorzy: Chung J. K. , Sahoo P. K.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we determine the general solution of the functional equation f(ux+vy, uy+vx) = g(x, y) h(u, v) where f, g, h: R2 -R are unknown functions. We also treat the equation f(ux + vy, uy + vx, zw) = g(x, y, z) h(u, v, w) where f,g, h : R3 -R are unknown functions. Our method is elementary and we do not use any regularity conditions.

Słowa kluczowe

EN

functional equations; multiplicative equations; matrix

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 539--544
• Opis fizyczny: Bibliogr. 2 poz.

Twórcy

autor

Chung J. K.

• Department of Applied Mathematics, South China University of Technology, Guangzhou, People's Republic of China

autor

Sahoo P. K.

• Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.

Bibliografia

• [1] J . Aczél, J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.
• [2] P. K. Sahoo, T. Riedel, Mean Value Theorems and Functional Equations, World Scientific, Singapore, 1998.