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1 results

  • A minimum condition and some realted fixed-point theorems

  • Part of
  • Jacek R. Jachymski, James D. Stein, Jr
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 66 / Issue 2 / April 1999
    Published online by Cambridge University Press:
    09 April 2009, pp. 224-243
    Print publication:
    April 1999
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  • The classic Banach Contraction Principle assumes that the self-map is a contraction. Rather than requiring that a single operator be a contraction, we weaken this hypothesis by considering a minimum involving a set of iterates of that operator. This idea is a central motif for many of the results of this paper, in which we also study how this weakended hypothesis may be applied in Caristi's theorem, and how combinatorial arguments may be used in proving fixed-point theorems.