Exact(60)
Recently, there are some advances obtained for iterative roots.
Meanwhile, we construct infinite many iterative roots if they exist.
If n is even, then F has no iterative roots.
The problem of iterative roots for strictly monotone self-mappings has been well solved.
They proved that those iterative roots are (C^{1}) locally stable but (C^{1}) globally unstable.
We present sufficient and necessary conditions under which those multifunctions have nth iterative roots.
This equivalent condition and the construction method of nth iterative roots extend the previous results.
The following result gives the iterative roots of those functions with 1-extension.
In this section, we discuss the existence of iterative roots of F ∈ S 1.
However, Theorem 3.3 shows that F 6 has iterative roots of order n ≥ 2 on I.
By studying the iterative roots, people can find the missing information in the iterative process.
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