University of Louisville
On Two Functional Equations and Their Solutions
Institution
University of Louisville
Faculty Advisor/ Mentor
Prasanna Sahoo
Abstract
This poster will discuss the solutions of two functional equations that arise in connection with the characterizations of the determinant and permanent of symmetric two-by-two matrices. The general solutions f:R->R of the two functional equations f(ux-vy,uyvx)=f(x,y)+ f(u,v)+ f(x,y)f(u,v) and f(ux+vy,uy-vx)=f(x,y)+ f(u,v)+ f(x,y)f(u,v) for all x,y,u,v in R are determined. Also, the solutions of a more generalized functional equation are discussed.
On Two Functional Equations and Their Solutions
This poster will discuss the solutions of two functional equations that arise in connection with the characterizations of the determinant and permanent of symmetric two-by-two matrices. The general solutions f:R->R of the two functional equations f(ux-vy,uyvx)=f(x,y)+ f(u,v)+ f(x,y)f(u,v) and f(ux+vy,uy-vx)=f(x,y)+ f(u,v)+ f(x,y)f(u,v) for all x,y,u,v in R are determined. Also, the solutions of a more generalized functional equation are discussed.