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

Received 5 April 1994; Revised 29 September 1994

Copyright © 1995 Hiroshi Haruki and Themistocles M. Rassias. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.