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A composite functional equation from algebraic aspect

Burai, Pál and Házy, Attila and Juhász, Tibor (2013) A composite functional equation from algebraic aspect. Aequationes Mathematicae, 86 (1-2). pp. 57-64. ISSN 0001-9054 (print version), 1420-8903 (electronic version)

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Abstract

In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian group. This equation originates from Problem 10854 of the American Mathematical Monthly. We give an algebraic description of the solutions on uniquely 3-divisible Abelian groups, and then we construct all solutions f of this equation on finite Abelian groups without elements of order 3 and on divisible Abelian groups without elements of order 3 including the additive group of real numbers.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra
Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis
Depositing User: Dr. Attila/A Házy
Date Deposited: 03 Oct 2015 16:06
Last Modified: 03 Oct 2015 16:08
URI: http://real.mtak.hu/id/eprint/29492

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