One-dimensional Functional Equations - Belitskii, Genrich (Birkhäuser Basel, 2003)
This monograph is devoted to the study of functional equations g(x, <p(x), <p(Fl(X)), ... , <p(Fn(x))) = 0, x E M, (0.1) where M is either the real line lR or the unit circle lI', lR 1 is a given mapping. k We assume that the mappings f, F1, ... , Fn are of a class C , k E NU{ 00, ~}. According to the standard definition CO(M) is the class of continuous functions on M; Ck(M) with 0 < k < 00 consists of k-times continuously differentiable functions on M; COO(M) = n Ck(M) l