A composite functional equation from algebraic aspect

作者：Burai Pal^*; Hazy Attila; Juhasz Tibor

来源：Aequationes Mathematicae, 2013, 86(1-2): 57-64.

DOI：10.1007/s00010-013-0211-0

• Composite functional equation
• iterative functional equation
• additive mapping
• automorphism
• Hamel basis
• Abelian group

In this paper we discuss the composite functional equation %26lt;br%26gt;f(x + 2f(y)) = f(x) + y + f(y) %26lt;br%26gt;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.

• 出版日期2013-9