scholarly journals The product property of the almost fixed point property for digital spaces

2021 ◽  
Vol 6 (7) ◽  
pp. 7215-7228
Author(s):  
Jeong Min Kang ◽  
◽  
Sang-Eon Han ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Product Property ◽  
Digital Spaces

scholarly journals Strengthened fixed point property and products in ordered sets

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Josef Niederle
Keyword(s):  
Fixed Point ◽  
Axiom Of Choice ◽  
Fixed Point Property ◽  
Point Property ◽  
Ordered Sets ◽  
Product Property ◽  
Chain Complete ◽  
The Axiom Of Choice

AbstractStrengthened fixed point property for ordered sets is formulated. It is weaker than the strong fixed point property due to Duffus and Sauer and stronger than the product property meaning that A × Y has the fixed point property whenever A has the former and Y has the latter. In particular, doubly chain complete ordered sets with no infinite antichain have the strengthened fixed point property whenever they have the fixed point property, which yields a transparent proof of the well-known theorem saying that doubly chain complete ordered sets with no infinite antichain have the product property whenever they have the fixed point property. The new proof does not require the axiom of choice.

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.

scholarly journals A product space with the fixed point property

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Helga Fetter Nathansky ◽  
Enrique Llorens-Fuster
Keyword(s):  
Fixed Point ◽  
Product Space ◽  
Fixed Point Property ◽  
Point Property
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