Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] W. Boyce, On $ \Gamma $-compact maps on an interval and commutativity. Trans. Amer. Math. Soc. 160 (1971), 87-102. MR 0280655 (43:6374)
  • [2] T. Mitchell, Common fixed points for equicontinuous families of mappings, Proc. Amer. Math. Soc. 33 (1972), 146-150. MR 0289735 (44:6923)
  • [3] A. Shields, On fixed points of commuting analytic functions, Proc. Amer. Math. Soc. 15 (1964), 703-706. MR 0165508 (29:2790)
  • [4] A. Schwartz, Common periodic points of commuting functions, Michigan Math. J. 12 (1965), 353-355. MR 0181996 (31:6221)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H25, 26A18

Retrieve articles in all journals with MSC: 54H25, 26A18

Additional Information

Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society