- ON THE SOLUTION OF A MULTI-VARIABLE BI-ADDITIVE FUNCTIONAL EQUATION I
- Park, Won-Gil ; Bae, Jae-Hyeong ;
- The Pure and Applied Mathematics, volume 13, issue 4, 2006, Pages 295~301
Abstract
We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.