scholarly journals Note on Common Fixed Point Theorems in Convex Metric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 28
Author(s):  
Anil Kumar ◽  
Aysegul Tas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Convex Metric Space ◽  
Correct Version ◽  
Convex Metric Spaces ◽  
Set Up ◽  
Common Fixed Point Theorems

In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

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.

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 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.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

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 in Intuitionistic Generalized Fuzzy Cone Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1212
Author(s):  
Mathuraiveeran Jeyaraman ◽  
Mookiah Suganthi ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results.

scholarly journals Coincidence and common fixed point theorems for four mappings satisfying (αs, F)-contraction

2018 ◽  
Vol 23 (5) ◽  
pp. 664-690 ◽  
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Mihai Postolache
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Common Solution ◽  
Type Integral ◽  
Common Fixed Point Theorems

In this paper, we manifest some coincidence and common fixed point theorems for four self-mappings satisfying Círíc-type and Hardy–Rogers-type (αs,F)-contractions defined on an αs-complete b-metric space. We apply these results to infer several new and old corresponding results in ordered b-metric spaces and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We present examples to validate our results. We discuss an application of main result to show the existence of common solution of the system of Volterra type integral equations.

scholarly journals Some common fixed point theorems for Ciric type contraction mappings

2012 ◽  
Vol 43 (2) ◽  
pp. 187-202
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Type Contraction

Some common fixed point theorems for \'{C}iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

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