Reducing the polynomial-like iterative equations order and a generalized Zoltán Boros' problem

Abstract

We present a technique for reducing the order of polynomial-like iterative equations; in particular, we answer a question asked by Wenmeng Zhang and Weinian Zhang. Our method involves the asymptotic behaviour of the sequence of consecutive iterates of the unknown function at a given point. As an application we solve a problem of Zoltán Boros posed during the 50th ISFE (2012).