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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a fixed point theorem of Kirk
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by Claudio H. Morales and Simba A. Mutangadura
Proc. Amer. Math. Soc. 123 (1995), 3397-3401
DOI: https://doi.org/10.1090/S0002-9939-1995-1301520-6

Abstract:

Let X be a reflexive Banach space, D an open and bounded subset of X, and $T:\bar D \to X$ a continuous mapping which is locally pseudocontractive on D. Suppose there exists an element $z \in D$ such that $\left \| {z - Tz} \right \| < \left \| {x - Tx} \right \|$ for all x on the boundary of D. Then under the so-called condition (S), T has a fixed point in D. Although this result was proved earlier by Kirk, we show here a much easier approach.
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 3397-3401
  • MSC: Primary 47H10
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1301520-6
  • MathSciNet review: 1301520