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A note on Kellogg's uniqueness theorem for fixed points


Author: Louis A. Talman
Journal: Proc. Amer. Math. Soc. 69 (1978), 248-250
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1978-0467416-7
MathSciNet review: 0467416
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Abstract: In 1975, R. B. Kellogg gave a condition guaranteeing uniqueness for the fixed point whose existence is insured by the Schauder Theorem. In this note, we indicate how to extend Kellogg's result to the class of k-set-contractions.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0467416-7
Keywords: Fixed point, fixed point index, k-set-contraction, measure of noncompactness, $ \alpha $-Lipschitz operator, degree theory
Article copyright: © Copyright 1978 American Mathematical Society

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