Continuously decreasing solutions for polynomial-like iterative equations

Abstract

Most known results on existence, uniqueness and stability for solutions of the polynomial-like iterative equation Σi=1n λifi(x) = F(x) were obtained in the case of λ1 ≠ 0. In this paper, we construct C0 decreasing solutions of the iterative equation in the case that λ1 can vanish to answer the Leading Coefficient Problem. Moreover, we also give the necessary and sufficiently condition for uniqueness of solutions. © 2013 Science China Press and Springer-Verlag Berlin Heidelberg.