scholarly journals Note on the Hahn-Banach Theorem in a Partially Ordered Vector Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Toshiharu Kawasaki ◽  
Masashi Toyoda ◽  
Toshikazu Watanabe
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Range Space ◽  
Partially Ordered ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space ◽  
Banach Theorem

Using a fixed point theorem in a partially ordered set, we give a new proof of the Hahn-Banach theorem in the case where the range space is a partially ordered vector space.

scholarly journals Another proof of the Browder–Göhde–Kirk theorem via ordering argument

2002 ◽  
Vol 65 (1) ◽  
pp. 105-107 ◽  
Author(s):  
Jacek Jachymski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Nonexpansive Mappings ◽  
Partially Ordered ◽  
Common Fixed Point Theorem

Using the Zermelo Principle, we establish a common fixed point theorem for two progressive mappings on a partially ordered set. This result yields the Browder–Göhde–Kirk fixed point theorem for nonexpansive mappings.

Bound Sets in Partial Orders and the Fixed Point Property

1987 ◽  
Vol 30 (4) ◽  
pp. 421-428 ◽  
Author(s):  
Hartmut Höft
Keyword(s):  
Fixed Point ◽  
Partially Ordered Set ◽  
Fixed Point Theorems ◽  
Ordered Set ◽  
Extension Property ◽  
Fixed Point Property ◽  
Point Property ◽  
Maximal Elements ◽  
Partially Ordered ◽  
Bound Sets

AbstractIn this paper we introduce several properties closely related to the fixed point property of a partially ordered set P: the comparability property, the fixed point property for cones, and the fixed point extension property. We apply these properties to the sets of common bounds of the minimal (maximal) elements of the partially ordered set P in order to derive fixed point theorems for P.

scholarly journals Three counterexamples concerning ω-chain completeness and fixed point properties

1981 ◽  
Vol 24 (2) ◽  
pp. 141-146 ◽  
Author(s):  
J. D. Mashburn
Keyword(s):  
Fixed Point ◽  
Upper Bound ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered ◽  
Fixed Point Properties ◽  
Countable Chain ◽  
Chain Complete

A partially ordered set, is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.

scholarly journals Some Common Fixed Point Theorems in Partially Ordered Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Khadija Bouzkoura ◽  
Said Benkaddour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Common Fixed Point Theorems

The purpose of this paper is to prove some new fixed point theorem and common fixed point theorems of a commuting family of order-preserving mappings defined on an ordered set, which unify and generalize some relevant fixed point theorems.

The order-bound topology

1972 ◽  
Vol 71 (2) ◽  
pp. 321-327 ◽  
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Vector Space ◽  
Positive Cone ◽  
Order Topology ◽  
Bounded Subset ◽  
Partially Ordered ◽  
Convex Topology ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space ◽  
Locally Convex Topology ◽  
Locally Convex

Let (E, C) be a partially ordered vector space with positive cone C. The order-bound topology Pb(6) (order topology in the terminology of Schaefer(9)) on E is the finest locally convex topology for which every order-bounded subset of E is topologically bounded.

Sign in / Sign up

Export Citation Format

Share Document