Common fixed points for a class of commuting mappings on an interval
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- by J. Cano PDF
- Proc. Amer. Math. Soc. 86 (1982), 336-338 Request permission
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.References
- William M. Boyce, $\Gamma$-compact maps on an interval and fixed points, Trans. Amer. Math. Soc. 160 (1971), 87–102. MR 280655, DOI 10.1090/S0002-9947-1971-0280655-1
- Theodore Mitchell, Common fixed-points for equicontinuous semigroups of mappings, Proc. Amer. Math. Soc. 33 (1972), 146–150. MR 289735, DOI 10.1090/S0002-9939-1972-0289735-4
- Allen L. Shields, On fixed points of commuting analytic functions, Proc. Amer. Math. Soc. 15 (1964), 703–706. MR 165508, DOI 10.1090/S0002-9939-1964-0165508-3
- A. J. Schwartz, Common periodic points of commuting functions, Michigan Math. J. 12 (1965), 353–355. MR 181996
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 336-338
- MSC: Primary 54H25; Secondary 26A18
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667301-2
- MathSciNet review: 667301