MathDB

We denote by \mathbb{R}^\plus{} the set of all positive real numbers.
Find all functions f: \mathbb R^ \plus{} \rightarrow\mathbb R^ \plus{} which have the property: f(x)f(y)\equal{}2f(x\plus{}yf(x)) for all positive real numbers

x

and

y

.
Proposed by Nikolai Nikolov, Bulgaria

Problem Statement