scholarly journals Weak compactness and fixed point property for affine mappings

2004 ◽  
Vol 209 (1) ◽  
pp. 1-15 ◽  
Author(s):  
T.Domı́nguez Benavides ◽  
M.A.Japón Pineda ◽  
S. Prus
Keyword(s):  
Fixed Point ◽  
Weak Compactness ◽  
Fixed Point Property ◽  
Point Property ◽  
Affine Mappings

scholarly journals On Fixed Point Property under Lipschitz and Uniform Embeddings

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Jichao Zhang ◽  
Lingxin Bao ◽  
Lili Su
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Convex Sets ◽  
Fixed Point Property ◽  
Point Property ◽  
Lipschitz Mappings ◽  
Affine Mappings ◽  
Reflexive Space ◽  
Gateaux Differentiability

We first present a generalization of ω⁎-Gâteaux differentiability theorems of Lipschitz mappings from open sets to those closed convex sets admitting nonsupport points and then show that every nonempty bounded closed convex subset of a Banach space has the fixed point property for isometries if it Lipschitz embeds into a super reflexive space. With the application of Baudier-Lancien-Schlumprecht’s theorem, we finally show that every nonempty bounded closed convex subset of a Banach space has the fixed point property for continuous affine mappings if it uniformly embeds into the Tsirelson space T⁎.

Renormings and fixed point property in non-commutative -spaces II: Affine mappings

2012 ◽  
Vol 75 (13) ◽  
pp. 5357-5361 ◽  
Author(s):  
Carlos A. Hernández-Linares ◽  
Maria A. Japón
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Affine Mappings

scholarly journals Weak compactness is not equivalent to the fixed point property in c

2015 ◽  
Vol 431 (1) ◽  
pp. 471-481 ◽  
Author(s):  
Torrey Gallagher ◽  
Chris Lennard ◽  
Roxana Popescu
Keyword(s):  
Fixed Point ◽  
Weak Compactness ◽  
Fixed Point Property ◽  
Point Property

scholarly journals Komlós’ theorem and the fixed point property for affine mappings

2018 ◽  
Vol 146 (12) ◽  
pp. 5311-5322 ◽  
Author(s):  
Tomás Domínguez Benavides ◽  
Maria A. Japón
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Affine Mappings

scholarly journals Brush spaces and the fixed point property

2011 ◽  
Vol 158 (8) ◽  
pp. 1085-1089 ◽  
Author(s):  
M.M. Marsh ◽  
J.R. Prajs
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

Sign in / Sign up

Export Citation Format

Share Document