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 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.

Partial Orders on the 2-Cell

1975 ◽  
Vol 18 (3) ◽  
pp. 411-416
Author(s):  
E. D. Tymchatyn
Keyword(s):  
Partial Order ◽  
Metric Space ◽  
Closed Subset ◽  
Cartesian Product ◽  
Partial Orders ◽  
Partial Ordering ◽  
Compact Metric Space ◽  
Partially Ordered ◽  
Ordered Space

A partially ordered space is an ordered pair (X, ≤) where X is a compact metric space and ≤ is a partial ordering on X such that ≤ is a closed subset of the Cartesian product X×X. ≤ is said to be a closed partial order on X.

scholarly journals Contractive Mapping in Generalized, Ordered Metric Spaces with Application in Integral Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
L. Gholizadeh ◽  
R. Saadati ◽  
W. Shatanawi ◽  
S. M. Vaezpour
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered

We consider the concept of -distance on a complete, partially ordered -metric space and prove some fixed point theorems. Then, we present some applications in integral equations of our obtained results.

scholarly journals Common fixed point of g-approximative multivalued mapping in partially ordered metric space

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1173-1182 ◽  
Author(s):  
Mujahid Abbas ◽  
Ali Erduran
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered

In this paper, we introduce g-approximative multivalued mappings. Based on this definition, we gave some new definitions. Further, common fixed point results for g-approximative multivalued mappings satisfying generalized contractive conditions are obtained in the setup of ordered metric spaces. Our results generalize Theorems 2.6-2.9 given in ([1]).

scholarly journals Endpoints of multi-valued weakly contraction in complete metric spaces endowed with graphs

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4319-4329 ◽  
Author(s):  
Jukrapong Tiammee ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered

In this paper, we introduce a new concept of weak G-contraction for multi-valued mappings on a metric space endowed with a directed graph. Endpoint theorem of this mapping is established under some sufficient conditions in a complete metric space endowed with a directed graph. Our main results extend and generalize those fixed point in partially ordered metric spaces. Some examples supporting our main results are also given. Moreover, we apply our main results to obtain some coupled fixed point results in the context of complete metric spaces endowed with a directed graph which are more general than those in partially ordered metric spaces.

scholarly journals Best proximity point theorems for G-proximal weak contractions in complete metric spaces endowed with graphs

2018 ◽  
Vol 34 (1) ◽  
pp. 65-75
Author(s):  
CHALONGCHAI KLANARONG ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Special Case

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained.

On the Non-Cutpoint Existence Theorem

1968 ◽  
Vol 11 (2) ◽  
pp. 213-216 ◽  
Author(s):  
L. E. Ward
Keyword(s):  
Partial Order ◽  
Existence Theorem ◽  
Hausdorff Space ◽  
Fundamental Result ◽  
Partially Ordered ◽  
Ordered Space ◽  
Partially Ordered Spaces ◽  
Connected Spaces

The theorem of the title asserts that every non-degenerate continuum (that is, every compact connected Hausdorff space containing more than one point) contains at least two non-cutpoints. This is a fundamental result in set - theoretic topology and several standard proofs, each varying from the others to some extent, have been published. (See, for example, [1], [4] and [5]). The author has presented a less standard proof in [3] where the non-cutpoint existence theorem was obtained as a corollary to a result on partially ordered spaces. In this note a refinement of that argument is offered which seems to the author to be the simplest proof extant. To facilitate its exposition, the notion of a weak partially ordered space is introduced and the cutpoint partial order of connected spaces is reviewed.

scholarly journals Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

Meir–Keeler type contractive mappings in modular and partial modular metric spaces

2019 ◽  
Vol 13 (05) ◽  
pp. 2050087
Author(s):  
Hasan Hosseinzadeh ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Modular Metric Space ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Modular Metric Spaces ◽  
Contractive Mappings

In this paper, first, we introduce the class of [Formula: see text]-Meir–Keeler contractive mappings and establish some fixed point results. Next, we introduce the notion of partial modular metric space and establish some fixed point results in this new spaces. As consequences of these results, we deduce some fixed point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. Some examples are furnished to demonstrate the validity of the obtained results.

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