Fixed point theorems for certain classes of multifunctions

Author:
R. E. Smithson

Journal:
Proc. Amer. Math. Soc. **31** (1972), 595-600

DOI:
https://doi.org/10.1090/S0002-9939-1972-0288750-4

MathSciNet review:
0288750

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Abstract | References | Additional Information

Abstract: The following two fixed point theorems for multi-functions are proved: Theorem. *If* *is a tree and if* *is a lower semicontinuous multifunction such that* *is connected for each* , *then* *has a fixed point*. Theorem. *Let* *be a topologically chained, acyclic space in which every nest of topological chains is contained in a topological chain*. *If* *is a point closed multi-function such that the image of a topological chain is chainable and such that* *is either closed or chainable for each* , *then* *has a fixed point*.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0288750-4

Keywords:
Fixed point theorems for multifunctions,
tree,
arcwise connected spaces,
topologically chained spaces,
lower semicontinuous multifunctions

Article copyright:
© Copyright 1972
American Mathematical Society