Abstract
An open question was raised by Zhang-Yang in 1983: Does a PM function F with height 1 have an iterative root f of an order n≤N(F)+1 if the ‘characteristic endpoints condition’ is not satisfied? When F is strictly increasing on its characteristic interval K(F), this question was answered in the case n∈{N(F),N(F)+1} and the case n≤N(F)+1 for f increasing on K(F) and for f decreasing on K(F) with H(f)<n−1 respectively. In this paper we work on this question for F increasing on K(F) in some remaining cases. In the case n<N(F) and the case n≤N(F)+1 we discuss existence and nonexistence of f with H(f)=n and H(f)=n−1 respectively.
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