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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On continuity of fixed points of collectively condensing maps

Author: Martin Fan Cheng
Journal: Proc. Amer. Math. Soc. 63 (1977), 74-76
MSC: Primary 47H10; Secondary 54H25
MathSciNet review: 0435943
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Abstract: In this paper, we prove, in two parts, the following claim. Let X be a Banach space and $ \Lambda $ an arbitrary topological space. Suppose that $ T:\Lambda \times X \to X$ is collectively condensing; then the fixed point set $ S(\lambda ,y)$ has closed graph if and only if T is continuous in both $ \lambda $ and y.

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PII: S 0002-9939(1977)0435943-3
Keywords: Collective condensing, closed graph, upper-semicontinuity
Article copyright: © Copyright 1977 American Mathematical Society