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 Σ =1 λ i f i (x) = F(x) were obtained in the case of λ 1 ≠ 0. In this paper, we construct C 0 decreasing solutions of the iterative equation in the case that λ 1 can vanish to answer the Leading Coefficient Problem. Moreover, we also give the necessary and sufficiently condition for uniqueness of solutions.