Partially Ordered Spaces and Metric Spaces

1965 ◽  
Vol 72 (6) ◽  
pp. 628 ◽  
Author(s):  
Ralph DeMarr
Keyword(s):  
Metric Spaces ◽  
Partially Ordered ◽  
Partially Ordered Spaces

Eckland and Bishop-Phelps variational principles in partially ordered spaces

2021 ◽  
pp. 234-240
Author(s):  
Zukhra T. Zhukovskaya ◽  
Tatiana V. Zhukovskaia ◽  
Olga V. Filippova
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Variational Principles ◽  
Optimization Theory ◽  
Order Relation ◽  
Extremal Problems ◽  
Partially Ordered ◽  
Ordered Space ◽  
Partially Ordered Spaces

In this paper, an assertion about the minimum of the graph of a mapping acting in partially ordered spaces is obtained. The proof of this statement uses the theorem on the minimum of a mapping in a partially ordered space from [A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy. Caristi-like condition and the existence of minima of mappings in partially ordered spaces // Journal of Optimization Theory and Applications. 2018. V. 180. Iss. 1, 48–61]. It is also shown that this statement is an analogue of the Eckland and Bishop-Phelps variational principles which are effective tools for studying extremal problems for functionals defined on metric spaces. Namely, the statement obtained in this paper and applied to a partially ordered space created from a metric space by introducing analogs of the Bishop-Phelps order relation, is equivalent to the classical Eckland and Bishop-Phelps variational principles.

scholarly journals Theorems for Boyd-Wong-Type Contractions in Ordered Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hassen Aydi ◽  
Wasfi Shatanawi ◽  
Mihai Postolache ◽  
Zead Mustafa ◽  
Nedal Tahat
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered

We give some fixed point results using an ICS mapping and involving Boyd-Wong-type contractions in partially ordered metric spaces. Our results generalize, extend, and unify several well-known comparable theorems in the literature. Also, we present some examples to support our results.

Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Jamshaid Ahmad ◽  
Muhammad Arshad ◽  
Pasquale Vetro
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Coupled Coincidence

Abstract.In this paper, we extend the coupled coincidence point theorems for a mixed

scholarly journals Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces

2012 ◽  
Vol 44 (3) ◽  
pp. 233-251 ◽  
Author(s):  
Erdal KARAPINAR ◽  
Hassen AYDI ◽  
Zead MUSTAFA
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper, we prove tripledcoincidence and common fixed point theorems for $F: X\times X\times X\to X$ and $g:X\to X$ satisfying almost generalized contractions in partially ordered metric spaces. The presented results generalize the theorem of Berinde and Borcut Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal 74(15) (2011)4889--4897. Also, some examples are presented.

scholarly journals Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

2017 ◽  
Vol 18 (2) ◽  
pp. 317 ◽  
Author(s):  
Mitrofan M Choban ◽  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
General Concept ◽  
Type Condition ◽  
Partially Ordered ◽  
Monotonicity Properties ◽  
Contraction Type ◽  
Partially Ordered Spaces

<p>We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on  spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.</p>

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