Asymptotic normal structure and fixed points of nonexpansive mappings
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- by J.-B. Baillon and R. Schöneberg PDF
- Proc. Amer. Math. Soc. 81 (1981), 257-264 Request permission
Abstract:
A mapping $f$ defined on a subset $X$ of a Banach space $E$ and taking values in $E$ is said to be nonexpansive if $\left | {f(x) - f(y)} \right | \leqslant \left | {x - y} \right |$ for all $x,y \in X$. In this paper we introduce a promising new geometric property of Banach spaces and show that it yields via a minor modification of known arguments a new fixed point theorem for nonexpansive mappings which includes Kirk’s famous result as well as a recent result of Karlovitz. We also discuss in detail a situation not covered by this result.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 257-264
- MSC: Primary 47H10; Secondary 46B20, 47H09
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593469-1
- MathSciNet review: 593469