On solutions of a common generalization of the Goła̧b–Schinzel equation and of the addition formulae

Abstract Under some additional assumptions we determine solutions of the equation f ( x + M ( f ( x ) ) y ) = f ( x ) ○ f ( y ) , where f : R → R is Lebesgue measurable or Baire measurable, M : R → R and ○ : R 2 → R . All three functions are unknown.