Analytic solutions of polynomial-like iterative functional equations with variable coefficients are discussed in the complex field ℂ by reducing to an auxiliary equation and by applying known results for systems of nonlinear functional equations of finite orders.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We discuss the Hyers-Ulam stability of the nonlinear iterative equation $G(f^{n₁}(x),...,f^{n_k}(x)) = F(x)$. By constructing uniformly convergent sequence of functions we prove that this equation has a unique solution near its approximate solution.