scholarly journals Fixed point property and approximation of a class of nonexpansive mappings

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Yisheng Song ◽  
Ying Huang
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
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.

scholarly journals Remarks on the stability of the fixed point property for nonexpansive mappings

2012 ◽  
Vol 1 (4) ◽  
pp. 417-430 ◽  
Author(s):  
Krzysztof Bolibok ◽  
Kazimierz Goebel ◽  
W. A. Kirk
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
The Stability

The fixed point property for some uniformly nonoctahedral Banach spaces

1999 ◽  
Vol 59 (3) ◽  
pp. 361-367 ◽  
Author(s):  
A. Jiménez-Melado
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Unit Sphere ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property

Roughly speaking, we show that a Banach space X has the fixed point property for nonexpansive mappings whenever X has the WORTH property and the unit sphere of X does not contain a triangle with sides of length larger than 2.

scholarly journals General Higher-Order Lipschitz Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Joseph Frank Gordon
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mappings ◽  
Higher Order ◽  
Fixed Point Property ◽  
Point Property ◽  
New Class ◽  
Lipschitz Mappings ◽  
Approximate Fixed Point Property

In this paper, we introduce a new class of mappings and investigate their fixed point property. In the first direction, we prove a fixed point theorem for general higher-order contraction mappings in a given metric space and finally prove an approximate fixed point property for general higher-order nonexpansive mappings in a Banach space.

scholarly journals The fixed-point property in Banach spaces containing a copy ofc0

2003 ◽  
Vol 2003 (3) ◽  
pp. 183-192
Author(s):  
Maria A. Japón Pineda
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Weak Topology ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Asymptotically Nonexpansive ◽  
Locally Convex Topology ◽  
Locally Convex

We prove that every Banach space containing an isomorphic copy ofc0fails to have the fixed-point property for asymptotically nonexpansive mappings with respect to some locally convex topology which is coarser than the weak topology. If the copy ofc0is asymptotically isometric, this result can be improved, because we can prove the failure of the fixed-point property for nonexpansive mappings.

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