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http://dx.doi.org/10.5831/HMJ.2012.34.3.375

ON A SYMMETRIC FUNCTIONAL EQUATION

Chung, Jae-Young (Department of Mathematics, Kunsan National University)

Publication Information

Honam Mathematical Journal / v.34, no.3, 2012 , pp. 375-379 More about this Journal

Abstract

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

Keywords

symmetric functional equation; additive function; measurable function;

Citations & Related Records

Reference

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