scholarly journals Common fixed point theorems for (ψ, φ)-weak nonlinear contraction in partially ordered sets

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Madjid Eshaghi Gordji ◽  
Hamid Baghani ◽  
Gwang Hui Kim
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Nonlinear Contraction ◽  
Common Fixed Point Theorems

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 Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 74 ◽  
Author(s):  
Haitham Qawaqneh ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Type Mapping ◽  
Admissible Mapping ◽  
Contraction Type ◽  
Common Fixed Point Theorems

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.

scholarly journals COMMON FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTION IN PARTIALLY ORDERED METRIC SPACE

2015 ◽  
Vol 11 (5) ◽  
pp. 5266-5275
Author(s):  
Gopi Prasad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Partially Ordered ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction

In this paper we prove some common fixed point theorems for two and four self-mappings using rational type contraction and some newly notified definitions in partially ordered metric space. In this way we generalized, modify, and extend some recent results due to Chandok and Dinu [14], Shantanwi and Postolache[28] and many others [1, 2, 4, 5, 21, 29, 30], thus generalizing results of Cabrea, Harjani and Sadarangani [12] as well as Dass and Gupta [15]  in the context of partial order metric setting.

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.

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