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On Rhoades' open questions


Authors: Shih-sen Chang and Qi Chun Zhong
Journal: Proc. Amer. Math. Soc. 109 (1990), 269-274
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1990-1007491-X
MathSciNet review: 1007491
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Abstract: In this paper the open questions raised by Rhoades [1] are answered or partially answered.


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

  • [1] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. MR 0433430 (55:6406)
  • [2] Shih-Sen Chang, On Rhoades' open questions and some fixed point theorems for a class of mappings, Proc. Amer. Math. Soc. 97 (1986), 343-346. MR 835895 (87e:54111)
  • [3] Qi-Chun Zhong, Fixed point theorems for (16) type contractive mappings, J. Math. Res. Exposition (4) 7 (1987), 555-558. MR 938229 (89b:54054)
  • [4] L. E. Taylor, A contractive mapping without fixed points, Notices Amer. Math. Soc. 24 (1977), A-649.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1007491-X
Keywords: Rhoades' open question, fixed point, periodic point, periodic index
Article copyright: © Copyright 1990 American Mathematical Society

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