Abstract

Gauss established a theory on the functional equation (Gauss' functional equation) f(a+b2,ab)=f(a,b)  (a,b>0), where f:R+×R+→R is an unknown function of the above equation.In this paper we treat the functional equation f(a+b2,2aba+b)=f(a,b)  (a,b>0) where f:R+×R+→R is an unknown function of this equation.The purpose of this paper is to prove new results on this functional equation by following the theory of Gauss' functional equation.