## 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.