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Proceedings of the American Mathematical Society

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A fixed point theorem for multifunctions in a locally convex space

Authors: V. M. Sehgal and Evelyn Morrison
Journal: Proc. Amer. Math. Soc. 38 (1973), 643-646
MSC: Primary 47H10; Secondary 54H25
MathSciNet review: 0312344
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Abstract: Let $ S$ be a convex subset of a locally convex space $ E$ and $ K$ a compact subset of $ S$. Let $ f:S \to F$ (a topological space) and $ g:K \to F$ be multifunctions. In this paper sufficient conditions are given for the existence of an $ x \in K$ such that $ f(x) \cap g(x) \ne \emptyset $. The result generalizes a recent theorem of Himmelberg (J. Math. Anal. Appl. 38 (1972), 205-207) and in special cases extends some of the other well-known results.

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Keywords: Multifunctions, upper semicontinuity, fixed point
Article copyright: © Copyright 1973 American Mathematical Society

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