Stability problem for the Goł¸ab–Schinzel type functional equations

Let X be a vector space over a field K of real or complex numbers, n ∈ N and λ ∈ K \ {0}. We study the stability problem for the Goł¸ab–Schinzel type functional equations 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. © 2007 Elsevier Inc. All rights reserved.