6533b82cfe1ef96bd12900ec
RESEARCH PRODUCT
On the structure of the set of equivalent norms on ℓ1 with the fixed point property
Maria A. JapónEnrique Llorens-fusterCarlos A. Hernandez Linaressubject
CombinatoricsDiscrete mathematicsRenorming theoryApplied MathematicsNorm (mathematics)Fixed-point theoremNonexpansive mappingsFixed point theoryEquivalence of metricsFixed-point propertyStabilityAnalysisMathematicsdescription
Abstract Let A be the set of all equivalent norms on l 1 which satisfy the FPP. We prove that A contains rays. In fact, every renorming in l 1 which verifies condition (⁎) in Theorem 2.1 is the starting point of a (closed or open) ray composed by equivalent norms on l 1 with the FPP. The standard norm ‖ ⋅ ‖ 1 or P.K. Linʼs norm defined in Lin (2008) [12] are examples of such norms. Moreover, we study some topological properties of the set A with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to ‖ ⋅ ‖ 1 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-03-01 | Journal of Mathematical Analysis and Applications |