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 Homeomorphisms related to the polynomial-like iterative equation on S^1 Pingping Zhang,Weinian Li,Weihong Sheng Keywords:Unit circle, homeomorphism, iterative equation, $C^0$ solution. Abstract: In this paper we study all homeomorphisms on the unit circle $\mathbb{S}^1$, whose lifts are $C^0$ solutions of a class of nonhomogeneous polynomial-like iterative equation. By an auxiliary equation, we present all those homeomorphisms and illustrate our results by examples.