A fixed point theorem and attractors

Authors:
Ludvik Janos and J. L. Solomon

Journal:
Proc. Amer. Math. Soc. **71** (1978), 257-262

MSC:
Primary 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1978-0482716-2

MathSciNet review:
0482716

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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate attractors for compact sets by considering a certain quotient space. The following theorem is included. Let , *G* a closed convex subset of a Banach space, *f* a mapping satisfying (i) there exists which is an attractor for compact sets under *f*; (ii) the family is equicontinuous. Then *f* has a fixed point.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0482716-2

Keywords:
Attractors for compact sets,
equicontinuous family,
quotient space,
contractive mapping,
retraction,
fixed point

Article copyright:
© Copyright 1978
American Mathematical Society