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Functional equation

Source: Iran 3rd round-2017-Algebra final exam-P1

September 2, 2017
algebrafunctional equation

Problem Statement

Let R≥0\mathbb{R}^{\ge 0} be the set of all nonnegative real numbers. Find all functions f:R≥0→R≥0f:\mathbb{R}^{\ge 0} \to \mathbb{R}^{\ge 0} such that x+2max⁡{y,f(x),f(z)}≥f(f(x))+2max⁡{z,f(y)} x+2 \max\{y,f(x),f(z)\} \ge f(f(x))+2 \max\{z,f(y)\} for all nonnegative real numbers x,yx,y and zz.
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