MathDB
functional equation: f(x+1/n)<f(x)+1/n

Source: Romanian District Olympiad 2016, Grade XI, Problem 3

October 5, 2018
functionalgebrafunctional equationcontinuityreal analysis

Problem Statement

Find the continuous functions f:RR f:\mathbb{R}\longrightarrow\mathbb{R} having the following property: f\left( x+\frac{1}{n}\right) \le f(x) +\frac{1}{n}, \forall n\in\mathbb{Z}^* , \forall x\in\mathbb{R} .