The existence theorem of a new multi-valued mapping in metric space endowed with graph

2017 ◽  
Vol 33 (2) ◽  
pp. 191-198
Author(s):  
ARAYA KHEAWBORISUT ◽  
◽  
SUTHEP SUANTAI ◽  
ATID KANGTUNYAKARN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Directed Graph ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Ordered Metric Spaces ◽  
New Type

In this paper, we introduce a new type of multi-valued G-contraction mapping on a metric space endowed with a directed graph G and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present.

scholarly journals The Kannan Contraction Mapping Theorem for Composition Operators in Metric Spaces and Partially Ordered Metric Spaces

2019 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Composition Operators ◽  
Contraction Mapping Theorem ◽  
Ordered Metric Spaces ◽  
Kannan Contraction

In this paper, fixed point theorems of the Kannan type are obtained in the setting of metric space and metric space endowed with partial order, respectively, for self-mappings that are composition operators.

scholarly journals Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Rectangular Metric Space ◽  
New Type ◽  
Symmetry Requirement ◽  
Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

Coupled coincidence and coupled common fixed point theorems on a fuzzy metric space with a graph

2018 ◽  
Vol 34 (3) ◽  
pp. 417-424
Author(s):  
PHUMIN SUMALAI ◽  
◽  
POOM KUMAM ◽  
DHANANJAY GOPAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric ◽  
Coupled Common Fixed Point ◽  
Common Fixed Point Theorems ◽  
Coupled Coincidence

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1–14], we introduce a new class of G − f−contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph.

scholarly journals Fixed Point Problems in Cone Rectangular Metric Spaces with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Muhammad Nazam ◽  
Anam Arif ◽  
Hasan Mahmood ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Implicit Relation ◽  
Rectangular Metric Space ◽  
Homotopy Result

In this paper, we introduce an ordered implicit relation and investigate some new fixed point theorems in a cone rectangular metric space subject to this relation. Some examples are presented as illustrations. We obtain a homotopy result as an application. Our results generalize and extend several fixed point results in literature.

scholarly journals Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Mi Zhou ◽  
Xiao-lan Liu ◽  
Nicolae Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weak Compatibility ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

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 On Best Proximity Points under the -Property on Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapinar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Point Of View ◽  
Ordered Metric Spaces

Very recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the -property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the -property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.

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 Coupled fixed point theorems for weakly compatible mappings along with $CLR$ property in Menger metric spaces

2016 ◽  
Vol 8 (2) ◽  
pp. 195-210
Author(s):  
L. Ben Aoua ◽  
A. Aliouche
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Fixed Point Problems ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Menger Metric Space

Coupled fixed point problems have attracted much attention in recent times. The aim of this paper is to extend the notions of E.A. property, CLR property and JCLR property for coupled mappings in Menger metric space and use this notions to generalizes the recent results of Jian-Zhong Xiao. The main result is supported by a suitable example.

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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