scholarly journals Some Coincidence and Common Fixed Point Results in Fuzzy Metric Space with an Application to Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saif Ur Rehman ◽  
Iqra Shamas ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fuzzy Metric ◽  
Weak Compatibility ◽  
Common Fixed Point Theorems

In this paper, we study some coincidence point and common fixed point theorems in fuzzy metric spaces by using three-self-mappings. We prove the uniqueness of some coincidence point and common fixed point results by using the weak compatibility of three-self-mappings. In support of our results, we present some illustrative examples for the validation of our work. Our results extend and improve many results given in the literature. In addition, we present an application of fuzzy differential equations to support our work.

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 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 Some fixed point theorems in fuzzy metric space

2008 ◽  
Vol 39 (4) ◽  
pp. 309-316 ◽  
Author(s):  
Urmila Mishra ◽  
Abhay Sharad Ranadive ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Reciprocal Continuity ◽  
Common Fixed Point Theorems

In this paper we prove common fixed point theorems in fuzzy metric spaces employing the notion of reciprocal continuity. Moreover we have to show that in the context of reciprocal continuity the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.

scholarly journals Some common fixed point theorems in fuzzy metric spaces using compatible of type A-1 and A-2

1970 ◽  
Vol 7 (1) ◽  
pp. 18-27
Author(s):  
CT Aage ◽  
JN Salunke
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type A ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Common Fixed Point Theorems

Recently M. S Khan, H. K. Pathak and R. George [9] have been introduced the concept of compatible of type A − 1 and type A − 2 and obtained some common fixed point theorems in fuzzy metric spaces. In this connection we have proved some common fixed point theorems in fuzzy metric space using semicompatible mappings. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5418 KUSET 2011; 7(1): 18-27

scholarly journals Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Saurabh Manro ◽  
Sanjay Kumar ◽  
S. S. Bhatia ◽  
Kenan Tas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems

This paper consists of main two sections. In the first section, we prove a common fixed point theorem in modified intuitionistic fuzzy metric space by combining the ideas of pointwiseR-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions. In the second section, we prove common fixed point theorems in modified intuitionistic fuzzy metric space from the class of compatible continuous mappings to noncompatible and discontinuous mappings. Lastly, as an application, we prove fixed point theorems using weakly reciprocally continuous noncompatible self-mappings on modified intuitionistic fuzzy metric space satisfying some implicit relations.

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

scholarly journals Fixed Point and Common Fixed Point Theorems on Ordered Cone b-Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sahar Mohammad Abusalim ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Common Fixed Point Theorems ◽  
Cone Metric

The concept of a cone b-metric space has been introduced recently as a generalization of a b-metric space and a cone metric space in 2011. The aim of this paper is to establish some fixed point and common fixed point theorems on ordered cone b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature to ordered cone b-metric spaces. Some supporting examples are given.

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