Stability of the generalized Gołąb--Schinzel equation

Summary

We determine all unbounded continuous solutions f : R → R of the inequality  | f (x+ f(x)^k y)- λ f(x)f(y) | ≦ ε ,  where k is a positive integer, λ is a real number and ε is a non-negative real number. As a consequence we obtain that in the class of continuous functions the generalized Gołąb--Schinzel equation is superstable.