Fixed point characterization of completeness on lattices for relatively isotone mappings
Jiří Klimeš (1984)
Archivum Mathematicum
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Jiří Klimeš (1984)
Archivum Mathematicum
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Klaus Heiner Kamps (1978)
Colloquium Mathematicae
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Katsuya Yokoi (2015)
Annales Polonici Mathematici
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This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence...
Podbrdský, Pavel, Pyrih, Pavel (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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J. Mioduszewski (1971)
Colloquium Mathematicae
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Heikkilä, S. (2010)
Fixed Point Theory and Applications [electronic only]
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Jiří Klimeš (1985)
Archivum Mathematicum
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D. W. Hajek, R. G. Wilson (1982)
Matematički Vesnik
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S. Parameshwara Bhatta (2005)
Czechoslovak Mathematical Journal
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In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.