Stability problem for the Goła̧b–Schinzel type functional equations

Let X be a vector space over a field K   of real or complex numbers, n∈Nn∈N and λ∈K∖{0}λ∈K∖{0}. We study the stability problem for the Goła̧b–Schinzel type functional equationsf(x+fn(x)y)=λf(x)f(y)f(x+f(x)ny)=λf(x)f(y) in the class of functions f:X→K such that the set {x∈X:f(x)≠0} has an algebraically interior point.