scholarly journals A Fixed Point Theorem in Orbitally Complete Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja ◽  
K. T. Kidane
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Contractive Condition ◽  
Ordered Sets ◽  
Ordered Metric Spaces ◽  
Partially Ordered

Let (X,⪯) be a partially ordered set and T:X→X be a mapping. We prove a fixed point theorem for the map T satisfying a contractive condition in orbits, when X is T-orbitally complete. Our result extends and generalizes the results of Samet et al. (2013) to partially ordered sets. Also, we generalize the results of Ran and Reurings (2004).

scholarly journals A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
J. Harjani ◽  
B. López ◽  
K. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type

The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of partially ordered metric spaces.

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.

scholarly journals Triple fixed point theorems for mixed monotone Presic-Kannan and Presic-Chatterjea mappings in partially ordered metric spaces

2014 ◽  
Vol 23 (2) ◽  
pp. 223-234
Author(s):  
MADALINA PACURAR ◽  
◽  
VASILE BERINDE ◽  
MARIN BORCUT ◽  
MIHAELA PETRIC ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered

The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings T : X → X to mappings F : X3 → X satisfying a Presiˇ c-Kannan type contractive condition: ... or a Presiˇ c-Chatterjea type contractive condition: ... The obtained tripled fixed point theorems extend and unify several related results in literature.

scholarly journals A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Xiangbing Zhou ◽  
Wenquan Wu ◽  
Hongjiang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010). We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.

A Theorem on Partially Ordered Sets, With Applications to Fixed Point Theorems

1961 ◽  
Vol 13 ◽  
pp. 78-82 ◽  
Author(s):  
Smbat Abian ◽  
Arthur B. Brown
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Point Theorems ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Prove Theorem ◽  
The Fixed Point Theorem ◽  
The Axiom Of Choice

In this paper the authors prove Theorem 1 on maps of partially ordered sets into themselves, and derive some fixed point theorems as corollaries.Here, for any partially ordered set P, and any mapping f : P → P and any point a ∈ P, a well ordered subset W(a) ⊂ P is constructed. Except when W(a) has a last element ε greater than or not comparable to f(ε), W(a), although constructed differently, is identical with the set A of Bourbaki (3) determined by a, f , and P1: {x|x ∈ P, x ≤ f(x)}.Theorem 1 and the fixed point Theorems 2 and 4, as well as Corollaries 2 and 4, are believed to be new.Corollaries 1 and 3 are respectively the well-known theorems given in (1, p. 54, Theorem 8, and Example 4).The fixed point Theorem 3 is that of (1, p. 44, Example 4); and has as a corollary the theorem given in (2) and (3).The proofs are based entirely on the definitions of partially and well ordered sets and, except in the cases of Theorem 4 and Corollary 4, make no use of any form of the axiom of choice.

scholarly journals Dedekind Completeness and a Fixed-Point Theorem

1957 ◽  
Vol 9 ◽  
pp. 400-405 ◽  
Author(s):  
E. S. Wolk
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Partially Ordered Sets ◽  
Natural Generalization ◽  
Ordered Sets ◽  
Natural Class ◽  
Partially Ordered ◽  
Usual Concept ◽  
Dedekind Completeness

McShane (5, 6) has introduced the concept of “Dedekind completeness” for partially ordered sets, which seems to be a natural generalization of the usual concept of completeness for lattices. It is the purpose of this paper to discuss some of the properties of Dedekind completeness, particularly with respect to a rather natural class of partially ordered sets which we call “uniform.”

scholarly journals A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
G. H. Kim
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Generalized Contraction ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contraction Type

We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.

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