Fixed point property of direct sums

• Main Authors: Dhompongsa S., Kaewcharoen A., Kaewkhao A.
• 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
• Institution: Chiang Mai University

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...