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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fixed points and boundaries
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by Eric Chandler PDF
Proc. Amer. Math. Soc. 82 (1981), 398-400 Request permission

Abstract:

A lemma of Ludvik Janos is used to show that if a nonexpansive self-map $T$ of a compact set $X$ is contractive on $\Delta ’X$, the boundary of $X$ in $\overline {{\text {co}}} X$, then $T$ has a fixed point in $X$. It is further proven that if $T(\Delta ’X) \cap \Delta ’X = \emptyset$, or if $T$ maps any point $y$ of $X$ away from $\Delta ’X$, then $T$ has a fixed point in $X$.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 82 (1981), 398-400
  • MSC: Primary 47H10; Secondary 47H09
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0612728-7
  • MathSciNet review: 612728