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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Common fixed points for a class of commuting mappings on an interval


Author: J. Cano
Journal: Proc. Amer. Math. Soc. 86 (1982), 336-338
MSC: Primary 54H25; Secondary 26A18
MathSciNet review: 667301
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Abstract: Let $ C$ be a family of continuous commuting functions of an interval $ I$ into itself. If each function, except for possibly one, has an interval $ [a,b],a \leqslant b$, for its set of fixed points or does not have periodic points except fixed ones, then it is shown that $ C$ has a common fixed point. This result generalizes a previous theorem of T. Mitchell.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0667301-2
PII: S 0002-9939(1982)0667301-2
Article copyright: © Copyright 1982 American Mathematical Society