Properties of fixed-point sets of nonexpansive mappings in Banach spaces
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- by Ronald E. Bruck PDF
- Trans. Amer. Math. Soc. 179 (1973), 251-262 Request permission
Abstract:
Let C be a closed convex subset of the Banach space X. A subset F of C is called a nonexpansive retract of C if either $F = \emptyset$ or there exists a retraction of C onto F which is a nonexpansive mapping. The main theorem of this paper is that if $T:C \to C$ is nonexpansive and satisfies a conditional fixed point property, then the fixed-point set of T is a nonexpansive retract of C. This result is used to generalize a theorem of Belluce and Kirk on the existence of a common fixed point of a finite family of commuting nonexpansive mappings.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 179 (1973), 251-262
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0324491-8
- MathSciNet review: 0324491