A new analogue of Gauss' functional equation

Hiroshi Haruki and Themistocles M. Rassias

International Journal of Mathematics and Mathematical Sciences, 1995, vol. 18, 1-8

Abstract:

Gauss established a theory on the functional equation (Gauss' functional equation) f ( a + b 2 , a b ) = 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 + b 2 , 2 a b a + 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.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:248590

DOI: 10.1155/S0161171295000962

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