ON A SYMMETRIC FUNCTIONAL EQUATION

• Journal title : Honam Mathematical Journal
• Volume 34, Issue 3,  2012, pp.375-379
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2012.34.3.375
Title & Authors
ON A SYMMETRIC FUNCTIONAL EQUATION
Chung, Jae-Young;

Abstract
We find a general solution $\small{f:G{\rightarrow}G}$ of the symmetric functional equation $\small{x+f(y+f(x))=y+f(x+f(y)),\;f(0)=0}$ where G is a 2-divisible abelian group. We also prove that there exists no measurable solution $\small{f:\mathbb{R}{\rightarrow}\mathbb{R}}$ of the equation. We also find the continuous solutions $\small{f:\mathbb{C}{\rightarrow}\mathbb{C}}$ of the equation.
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