On a Problem of Roger Cuculiere

Roman Ger

Abstract


In the February 2008 issue of  The American Mathematical Monthly (115, Problems and Solutions, p. 166) the following question was proposed by Roger Cuculiere:

Find all nondecreasing functions $f$ from $\mathbb{R}$ to $\mathbb{R}$ such that $f(x + f(y)) = f(f(x)) + f(y)$ for all real $x$ an $y$ (Problem 11345).
In the present paper we establish the general Lebesgue measurable solution, monotonic solutions as well as a description of the general solution of the functional equation in question.


Keywords


Cuachy type composite equation; measurable solutions; monotonic solutions; general solution

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DOI: http://dx.doi.org/10.26713%2Fjims.v1i2+%26+3.19

eISSN 0975-5748; pISSN 0974-875X