Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the structure of the fixed-point set of a nonexpansive mapping in a Banach space


Author: Ronald E. Bruck
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10

Retrieve articles in all journals with MSC: 47H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0428125-1
Keywords: Nonexpansive mapping, nonexpansive retraction
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society