International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 749-756
A new analogue of Gauss' functional equation
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.
Gauss established a theory on the functional equation (Gauss' functional equation)
where is an unknown function of the above equation.
In this paper we treat the functional equation
where 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.