Reducing the polynomial-like iterative equations order and a generalized Zolt\'an Boros' problem

TL;DR

This paper introduces a technique to reduce the order of polynomial-like iterative equations by analyzing the asymptotic behavior of iterates, successfully solving a problem posed by Zoltán Boros.

Contribution

It provides a novel method for simplifying polynomial-like iterative equations and addresses a previously open question in the field.

Findings

Effective order reduction technique demonstrated

Solved Boros' problem from 2012

Applicable to a class of polynomial-like equations

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 Zolt\'an Boros posed during the 50th ISFE (2012).