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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some fixed point theorems for condensing multifunctions in locally convex spaces

Authors: C. H. Su and V. M. Sehgal
Journal: Proc. Amer. Math. Soc. 50 (1975), 150-154
MSC: Primary 47H10
MathSciNet review: 0380530
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Abstract: Let $ G$ be a nonempty subset of a locally convex space $ E$ such that $ \operatorname{cl} (G)$ is convex and quasi-complete, and $ f:\operatorname{cl} (G) \to E$ a continuous condensing multifunction. In this paper, several fixed point theorems are established if $ f$ satisfies some conditions on the boundary of $ G$. The results herein extend some theorems of Reich [9] and generalize some of the well-known fixed point theorems.

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Keywords: Multifunction, condensing, fixed point, quasi-complete
Article copyright: © Copyright 1975 American Mathematical Society

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