On solutions of a common generalization of the Goł¸ab–Schinzel equation and of the addition formulae

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 ◦ : R2→R. All three functions are unknown. © 2007 Elsevier Inc. All rights reserved