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Functional Equation from Iran TST 2017

Source: 2017 Iran TST third exam day1 p3

April 26, 2017
algebrafunctional equationfunction

Problem Statement

Find all functions f:R+×R+→R+f: \mathbb {R}^+ \times \mathbb {R}^+ \to \mathbb {R}^+ that satisfy the following conditions for all positive real numbers x,y,z:x,y,z: f(f(x,y),z)=x2y2f(x,z)f\left ( f(x,y),z \right )=x^2y^2f(x,z) f(x,1+f(x,y))≥x2+xyf(x,x)f\left ( x,1+f(x,y) \right ) \ge x^2 + xyf(x,x)
Proposed by Mojtaba Zare, Ali Daei Nabi
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