International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 749-756
doi:10.1155/S0161171295000962
A new analogue of Gauss' functional equation
Hiroshi Haruki1
and Themistocles M. Rassias2
1Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Ontario, Waterloo N2L 3G1, Canada
2Department of Mathematics, University of La Verne, P.O. Box 51105, Kifissia, Athens 14510, Greece
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.