On the structure of the fixed-point set of a nonexpansive mapping in a Banach space
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- by Ronald E. Bruck PDF
- Proc. Amer. Math. Soc. 61 (1976), 16-18 Request permission
Abstract:
If $C$ is a closed convex subset of a reflexive, strictly convex Banach space $E$, and $T:C \to E$ is a nonexpansive mapping which has a fixed-point in the interior of $C$, then there exists a nonexpansive mapping ${T^{\ast }}:E \to E$ whose fixed-point set in $C$ is the fixed-point set of $T$.References
- Ronald E. Bruck Jr., A characterization of Hilbert space, Proc. Amer. Math. Soc. 43 (1974), 173–175. MR 341038, DOI 10.1090/S0002-9939-1974-0341038-7
- Ronald E. Bruck Jr., Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 251–262. MR 324491, DOI 10.1090/S0002-9947-1973-0324491-8
- D. G. de Figueiredo and L. A. Karlovitz, On the extension of contractions on normed spaces, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 95–104. MR 0275120
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 16-18
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0428125-1
- MathSciNet review: 0428125