On solutions of the Gołąb‐Schinzel equation

Abstract

We determine the solutions f : (0, ∞ ) → [0, ∞ ) of the functional equation f ( x + f ( x ) y ) = f ( x ) f ( y ) that are continuous at a point a > 0 such that f ( a ) > 0. This is a partial solution of a problem raised by Brzdęk.