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More maps for which $$F(T)=F(T^n)$$. (English) Zbl 1147.47041
The paper is a continuation of the authors’ recent article [in: Fixed point theory and applications 6, Nova Sci. Publ., New York, 71–105 (2007; Zbl 1209.47003)] on a comparison between fixed point sets of maps and fixed point sets of their iterations. Some new theorems on the equality $$\text{Fix}(T)= \text{Fix}(T^n)$$ for every $$n\geq 1$$ are presented. Generally speaking, the assumptions imply uniqueness of a fixed point [or a common fixed point]. The second part of each proof (the required equality) is always analogous and consists of some inequalities, implied by contraction-like assumptions, leading to a conclusion that any fixed point [resp., common fixed point] of an iteration is in fact the unique fixed point [resp., common fixed point] of a map.

##### MSC:
 47H10 Fixed-point theorems 47H04 Set-valued operators
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