MathDB

Find all functions

Source: 2009 Jozsef Wildt International Math Competition

April 17, 2020

functionfunctional equation

Problem Statement

Find all functions

f: (0, +\infty)\cap\mathbb{Q}\to (0, +\infty)\cap\mathbb{Q}

satisfying thefollowing conditions:
[*]

f(ax) \leq (f(x))^a

, for every

x\in (0, +\infty)\cap\mathbb{Q}

and

a \in (0, 1)\cap\mathbb{Q}

[*]

f(x+y) \leq f(x)f(y)

, for every

x,y\in (0, +\infty)\cap\mathbb{Q}