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
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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.References
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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