Almost all 1-set contractions have a fixed point

Butler, G. J.

doi:10.1090/S0002-9939-1979-0524316-2

Almost all $1$-set contractions have a fixed point
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by G. J. Butler PDF

Proc. Amer. Math. Soc. 74 (1979), 353-357 Request permission

Abstract:

The 1-set contractions and strict set contractions of a bounded, closed, convex subset C of a Banach space X are generalizations of the nonexpansive mappings and the Banach contractions of C, defined in terms of the measure of noncompactness of bounded subsets of X. Vidossich has shown that “almost all” nonexpansive mappings of C into itself have fixed points. In this note we establish a similar generic result for the 1-set contractions of C.

References

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Sur les espaces complets

15

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