Nonexpansive mappings on Banach lattices

Borwein, Jonathan M. and Sims, Brailey (1983) Nonexpansive mappings on Banach lattices. Comptes Rendus Mathématiques de l'Académie des Sciences, 5 . pp. 21-26.

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A mapping T defined on a weakly compact convex subset C of a Banach space X is said to be nonexpansive if ||T(x)-T(y)||≼||x-y|| for all x and y in C; and X is said to have the (weak) fixed point properly (FPP) if every such mapping has a fixed point. Classical results show that every uniformly convex Banach space and those with normal structure have the fixed point property. Until recently other positive results remained fragmentary. Moreover, it was only in 1981 that Alspach showed that L₁ does not have the FPP.

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 23 Feb 2015 13:55
Last Modified: 23 Feb 2015 13:55

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