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We present a technique for reducing the order of polynomial-like iterativeequations; in particular, we answer a question asked by Wenmeng Zhang andWeinian Zhang. Our method involves the asymptotic behaviour of the sequence ofconsecutive iterates of the unknown function at a given point. As anapplication we solve a problem of Zolt\'an Boros posed during the 50th ISFE(2012).

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