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

Under some additional assumptions we determine solutions of the equationf(x+M(f(x))y)=f(x)○f(y),f(x+M(f(x))y)=f(x)○f(y), where f:R→Rf:R→R is Lebesgue measurable or Baire measurable, M:R→RM:R→R and ○:R2→R○:R2→R. All three functions are unknown.