MathDB
functional inequality over R

Source: Mongolia MO 2000 Grade 10 P4

April 22, 2021
functional equationfeFunctional inequalityalgebra

Problem Statement

Suppose that a function f:R→Rf:\mathbb R\to\mathbb R satisfies the following conditions:
(i) ∣f(a)−f(b)∣≤∣a−b∣\left|f(a)-f(b)\right|\le|a-b| for all a,b∈Ra,b\in\mathbb R; (ii) f(f(f(0)))=0f(f(f(0)))=0.
Prove that f(0)=0f(0)=0.
Back to ProblemsView on AoPS