MathDB

Let

a,b,c

be non-zero distinct real numbers so that there exist functions

f,g:\mathbb{R}^{+} \to \mathbb{R}

so that:

af(xy)+bf(\frac{x}{y})=cf(x)+g(y)

For all positive real

x

and large enough

y

.
Prove that there exists a function

h:\mathbb{R}^{+} \to \mathbb{R}

so that:

f(xy)+f(\frac{x}{y})=2f(x)+h(y)

For all positive real

x

and large enough

y

Problem Statement