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Zbl 1117.47046
Petruşel, Gabriela
Cyclic representations and periodic points. (English)
[J] Stud. Univ. Babeş-Bolyai, Math. 50, No. 3, 107-112 (2005). ISSN 0252-1938; ISSN 2065-961X/e

The article deals with some results concerned with periodic points for some single-valued operators in metric spaces. The author presents the definition (due to I. A. Rus) of a fixed point structure and presents five theorems about the existence of $m$-periodic points. These theorems are based on an abstract lemma given by I. A. Rus; they are analogues of the classical Knaster-Tarski, Krasosel'skiĭ, Nemytskiĭ-Edelstein, Browder-Göhde-Kirk, Perov fixed point theorems. It should be remarked that the definition of a fixed point structure, in the author's formulation, is not completely clear, and so the same can be said about the theorems of the article.
[Peter Zabreiko (Minsk)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54H25 Fixed-point theorems in topological spaces

Keywords: periodic point; fixed point; cyclic representation; fixed point structure

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