Some fixed point theorems for compact maps and flows in Banach spaces.

Author:
W. A. Horn

Journal:
Trans. Amer. Math. Soc. **149** (1970), 391-404

MSC:
Primary 47.85

DOI:
https://doi.org/10.1090/S0002-9947-1970-0267432-1

MathSciNet review:
0267432

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be convex subsets of the Banach space *X*, with and closed and open in . If *f* is a compact mapping of into *X* such that and for some , then *f* has a fixed point in . (This extends a result of F. E. Browder published in 1959.) Also, if is a continuous flow on the Banach space *X*, are convex subsets of *X* with and compact and open in , and for some , where for all , then there exists such that for all . Minor extensions of Browder's work on ``nonejective'' and ``nonrepulsive'' fixed points are also given, with similar results for flows.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0267432-1

Keywords:
Banach space,
fixed points,
asymptotic fixed point theorems,
compact mappings,
flows,
nonejective fixed points,
nonrepulsive fixed points

Article copyright:
© Copyright 1970
American Mathematical Society