On a Problem of Roger Cuculiere

Authors

  • Roman Ger Instytut Matematyki, Uniwersytetu Slaskiego, ul. Bankowa 14, PL-40-007 Katowice, Poland

DOI:

https://doi.org/10.26713/jims.v1i2%20&%203.19

Keywords:

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

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.

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CITATION

How to Cite

Ger, R. (2009). On a Problem of Roger Cuculiere. Journal of Informatics and Mathematical Sciences, 1(2 & 3), 157–163. https://doi.org/10.26713/jims.v1i2 & 3.19

Issue

Vol. 1 No. 2 & 3 (2009)

Section

Research Articles

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