On a functional equation related to two-variable weighted quasi-arithmetic means

Tibor Kiss, Zsolt Páles

In this paper, we are going to describe the solutions of the functional equation $$\phi \left(\frac{x+y}{2}\right)(f(x)+f(y))=\phi (x)f(x)+\phi (y)f(y)$$ concerning the unknown functions $\phi$ an…