Fixed point theorems of the mappings of partially ordered sets

1971 ◽  
Vol 20 (2-3) ◽  
pp. 139-142 ◽  
Author(s):  
Alexander Abian
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

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.

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 Fixed point theorems for cyclic weak contractions in partially ordered sets endowed with a complete metric

2013 ◽  
Vol 29 (2) ◽  
pp. 179-186
Author(s):  
J. HARJANI ◽  
◽  
F. SABETGHADAM ◽  
K. SADARANGANI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

The purpose of this paper is to present some fixed point results for cyclic weak contractions in partially ordered sets endowed with a complete metric.

scholarly journals Global solutions to nonlinear second order interval integrodifferential equations by fixed point in partially ordered sets

2018 ◽  
Vol 37 (4) ◽  
pp. 153-172
Author(s):  
Robab Alikhani ◽  
Fariba Bahrani
Keyword(s):  
Fixed Point ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Partially Ordered Sets ◽  
Second Order ◽  
Partial Ordering ◽  
Order Interval ◽  
Ordered Sets ◽  
Partially Ordered

In this paper, we prove the existence and uniqueness of global solution for second order interval valued integrodifferential equation with initial conditions admitting only the existence of a lower solution or an upper solution. In this study, in order to make the global solution on entire $[0,b]$, we use a fixed point in partially ordered sets on the subintervals of $[0,b]$ and obtain local solutions. Also, under weak conditions we show being well-defined a special kind of  H-difference involved in this work. Moreover, we compare the results of existence and uniqueness under consideration of two kind of partial ordering on fuzzy numbers.

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