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Approximations and fixed points for condensing non-self-maps defined on a sphere


Author: Tzu-Chu Lin
Journal: Proc. Amer. Math. Soc. 105 (1989), 66-69
MSC: Primary 47H09; Secondary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1989-0973838-5
MathSciNet review: 973838
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Abstract: In this paper, we investigate the validity of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] defined on a sphere (the boundary of a closed ball) in an infinite-dimensional Banach space. We will prove that it is true for a continuous condensing map with suitable conditions posed. As applications of our theorem, some fixed point theorems of continuous condensing non-self-maps defined on a sphere are derived. Our results generalize some results of R. Nussbaum [10] and P. Massatt [8].


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DOI: https://doi.org/10.1090/S0002-9939-1989-0973838-5
Article copyright: © Copyright 1989 American Mathematical Society

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