区间上一类连续自映射的单调迭代根(英文)

The Monotone Iterative Roots of a Class of Self-Mappings on the Interval

英文关键词:continuous self-map  fixed point  iterative root.

中文摘要:

      设Ｉ＝［０，１］，０＜ａ＜ｂ＜１，记Φ_ab≡｛Ｆ∈Ｃ^０（Ｉ）：Ｆ｜［０，ａ］和Ｆ｜［ｂ，１］严格单调递增且Ｆ在［ａ，ｂ］恒取常值｝．本文讨论了Ｆ∈Φ_ab有单调迭代根的充要条件．

英文摘要:

      Let I = [0,1], 0 < a < b < 1. Let Φ_ab ≡ {F ∈ C⁰(I): both F|[0,a] and F|[b, 1] are strictly increasing, and F|[a, b] is constant }. In this paper we discuss necessary and sufficient conditions for F ∈Φ_ab to have monotone iterative roots.