scholarly journals On Fixed Point Results in Partial b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haitham Qawaqneh ◽  
Mohd Salmi Md Noorani ◽  
Hassen Aydi ◽  
Amjed Zraiqat ◽  
Arslan Hojat Ansari
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
The Self ◽  
Topological Properties ◽  
Triangular Inequality ◽  
Contraction Mappings ◽  
Symmetric Property

Partial b -metric spaces are characterised by a modified triangular inequality and that the self-distance of any point of space may not be zero and the symmetry is preserved. The spaces with a symmetric property have interesting topological properties. This manuscript paper deals with the existence and uniqueness of fixed point points for contraction mappings using triangular weak α -admissibility with regard to η and C -class functions in the class of partial b -metric spaces. We also introduce an example to demonstrate the obtained results.

scholarly journals On Some Boundedness and Convergence Properties of a Class of Switching Maps in Probabilistic Metric Spaces with Applications to Switched Dynamic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Fixed Point ◽  
Dynamic Systems ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
The Self ◽  
Convergence Properties ◽  
Probabilistic Metric Spaces ◽  
Switching Law ◽  
Probabilistic Metric

This paper investigates some boundedness and convergence properties of sequences which are generated iteratively through switched mappings defined on probabilistic metric spaces as well as conditions of existence and uniqueness of fixed points. Such switching mappings are built from a set of primary self-mappings selected through switching laws. The switching laws govern the switching process in between primary self-mappings when constructing the switching map. The primary self-mappings are not necessarily contractive but if at least one of them is contractive then there always exist switching maps which exhibit convergence properties and have a unique fixed point. If at least one of the self-mappings is nonexpansive or an appropriate combination given by the switching law is nonexpansive, then sequences are bounded although not convergent, in general. Some illustrative examples are also given.

scholarly journals Recent Fixed-Point Results for θ − Contraction Mappings in Rectangular M − Metric Spaces with Supportive Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mustafa Mudhesh ◽  
Hasanen A. Hammad ◽  
Habes Alsamir ◽  
Muhammad Arshad ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Theoretical Result ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Uniqueness Of The Solution

The goal of this manuscript is to present a new fixed-point theorem on θ − contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences with θ − contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).

scholarly journals Some fixed point results for $ \alpha $-admissible extended $ \mathcal{Z} $-contraction mappings in extended rectangular $ b $-metric spaces

2021 ◽  
Vol 7 (3) ◽  
pp. 3701-3718
Author(s):  
Yan Sun ◽  
◽  
Xiao-lan Liu ◽  
Jia Deng ◽  
Mi Zhou ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Contraction Mappings

<abstract><p>In this paper, we introduce $ \alpha $-admissible extended $ \mathcal{Z} $-contraction in the extended rectangular $ b $-metric spaces, then we provide some other conditions in Theorem 3.1, which are different from that in Chifu et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, and obtain the existence and uniqueness of fixed point in such spaces. Moreover, some examples are given to show the validity of our main theorems, and we give some corollaries related to our main results. As an application, we apply our main results to solve the existence of solutions for a class of boundary value problems of second order ordinary differential equations.</p></abstract>

scholarly journals Fixed point results concerning α-F-contraction mappings in metric spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 81 ◽  
Author(s):  
Lakshmi Kanta Dey ◽  
Poom Kumam ◽  
Tanusri Senapati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Contraction Mappings

<p>In this paper, we introduce the notions of generalized α-F-contraction and modified generalized α-F-contraction. Then, we present sufficient conditions for existence and uniqueness of fixed points for the above kind of contractions. Necessarily, our results generalize and unify several results of the existing literature. Some examples are presented to substantiate the usability of our obtained results.</p>

scholarly journals Double controlled quasi metric-like spaces and some topological properties of this space

2021 ◽  
Vol 6 (10) ◽  
pp. 11584-11594
Author(s):  
A. M. Zidan ◽  
◽  
Z. Mostefaoui ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Self ◽  
Topological Properties ◽  
New Type

<abstract><p>In present paper, we introduce a new extension of the double controlled metric-like spaces, so called double controlled quasi metric-like spaces "assuming that the self-distance may not be zero". Also, if the value of the metric is zero, then it has to be "a self-distance". After that, by using this new type of quasi metric spaces, we generalize many results in the literature and we prove fixed point theorems along with some examples illustrating.</p></abstract>

scholarly journals Multivalued weak cyclic δ-contraction mappings

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pulak Konar ◽  
Samir Kumar Bhandari ◽  
Sumit Chandok ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Cyclic Contraction ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
New Type

AbstractIn this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

SOME FIXED POINT RESULTS FOR A GENERALIZED $\psi$-WEAK CONTRACTION MAPPINGS IN b-METRIC SPACES

2021 ◽  
Vol 10 (5) ◽  
pp. 2449-2468
Author(s):  
E. Bashayreh ◽  
A. Talafhah ◽  
W. Shatanawi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Contraction Mappings

In this paper, we will present the definitions and notation of generalized $\psi$-weak contraction mappings in b-metric spaces, and establish some results besides the most important properties of fixed point in orbitally complete b-metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we generalize the results of Shatanawi [7]. Some examples are given to illustrate the useability of our results.

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