6533b824fe1ef96bd1281302
RESEARCH PRODUCT
Fixed point properties and proximinality in Banach spaces
P. Lorenzo RamírezEnrique Llorens-fusterT. Domínguez BenavidesJ. García Falsetsubject
Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApplied MathematicsRegular polygonBanach spaceCenter (group theory)Star (graph theory)Fixed pointCompact spaceBounded functionCoincidence pointAnalysisMathematicsdescription
Abstract In this paper we prove the existence of a fixed point for several classes of mappings (mappings admitting a center, nonexpansive mappings, asymptotically nonexpansive mappings) defined on the closed convex subsets of a Banach space satisfying some proximinality conditions. In particular, we derive a sufficient condition, more general than weak star compactness, such that if C is a bounded closed convex subset of l 1 satisfying this condition, then every nonexpansive mapping T : C → C has a fixed point.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-09-01 | Nonlinear Analysis: Theory, Methods & Applications |