More maps for which \(F(T)=F(T^n)\). (English) Zbl 1147.47041

Jeong, G. S.; Rhoades, B. E.

Demonstr. Math. 40, No. 3, 671-680 (2007).

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.

Reviewer: Grzegorz Gabor (Toruń)

MSC:

47H10	Fixed-point theorems
47H04	Set-valued operators

Keywords:

commuting maps; D-metric spaces; fixed points; multivalued maps; 2-metric spaces

Citations:

Zbl 1209.47003