Fixed point property of direct sums
For a uniformly convex space Z, we show that Z-direct sums (X1⊕⋯⊕XN)Z of Banach spaces X1,...,XN with R(a,Xi)<1+a for some a ∈(0,1] have the fixed point property for nonexpansive mappings. As a direct consequence, the result holds for all ψ-direct sums with ψ being strictly convex. The same resul...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2014
|
| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-28044438707&partnerID=40&md5=c24707ee3c75db04bfaffdc7706a32f1 http://cmuir.cmu.ac.th/handle/6653943832/4924 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | For a uniformly convex space Z, we show that Z-direct sums (X1⊕⋯⊕XN)Z of Banach spaces X1,...,XN with R(a,Xi)<1+a for some a ∈(0,1] have the fixed point property for nonexpansive mappings. As a direct consequence, the result holds for all ψ-direct sums with ψ being strictly convex. The same result is extended to all ψ-direct sums X⊕ψY of spaces X and Y with property (M), whenever ψ≠ψ1. The permanence of properties that are sufficient for the fixed point property are obtained for Z-direct sums (and then for ψ-direct sums). Such properties include the properties R(X)<2, WNUS, CNJ(a,X)<2, UKK, and NUC. © 2005 Elsevier Ltd. All rights reserved. |
|---|