On a functional equation on groups

Jukang K. Chung; Soon-Mo Jung; Prasanna K. Sahoo

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J. Korean Math. Soc. 2001; 38(1): 37-47

Printed January 1, 2001

On a functional equation on groups

Jukang K. Chung, Soon-Mo Jung, and Prasanna K. Sahoo

South China University of Technology, Hong-Ik University, University of Louisville

Abstract

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Abstract

We present the general solution of the functional equation
\begin{align*} &\ f(x_1 y_1 , x_2 y_2 ) + f(x_1 y_1^{-1} , x_2 ) + f( x_1 , x_2 y_2^{-1} )\\
= &\ f(x_1 y_1^{-1} , x_2 y_2^{-1} ) + f(x_1 y_1 , x_2 ) + f( x_1 , x_2 y_2 ). \end{align*} Furthermore, we also prove the Hyers-Ulam stability of the above functional equation.

Keywords: functional equations, Hyers-Ulam stability

MSC numbers: 39B32, 39B82