scholarly journals On (ϕ, ψ)-Metric Spaces with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1459
Author(s):  
Eskandar Ameer ◽  
Hassen Aydi ◽  
Hasanen A. Hammad ◽  
Wasfi Shatanawi ◽  
Nabil Mlaiki
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Two Dimensions ◽  
Topological Properties ◽  
Natural Topology ◽  
Fredholm Type ◽  
Banach Contraction ◽  
Type Integral ◽  
The Banach Contraction Principle ◽  
Space Concept

The aim of this article is to introduce the notion of a ϕ,ψ-metric space, which extends the metric space concept. In these spaces, the symmetry property is preserved. We present a natural topology τϕ,ψ in such spaces and discuss their topological properties. We also establish the Banach contraction principle in the context of ϕ,ψ-metric spaces and we illustrate the significance of our main theorem by examples. Ultimately, as applications, the existence of a unique solution of Fredholm type integral equations in one and two dimensions is ensured and an example in support is given.

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.

scholarly journals Geraghty Type Generalized F-Contractions and Related Applications in Partial b-Metric Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Deepak Singh ◽  
Varsha Chauhan ◽  
R. Wangkeeree
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
First Order ◽  
New Concepts ◽  
Banach Contraction ◽  
Uniqueness Of A Solution ◽  
The Banach Contraction Principle

The purpose of this paper is to introduce new concepts of (α,β)-admissible Geraghty type generalized F-contraction and to prove that some fixed point results for such mappings are in the perspective of partial b-metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic F-contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial b-metric space. Moreover, some examples are presented to illustrate the usability of the new theory.

scholarly journals COINCIDENCE AND COMMON FIXED POINT THEOREMS IN Ƒ-METRIC SPACES

2020 ◽  
Vol 4 (3) ◽  
pp. 43-49
Author(s):  
Demet Binbaşıoğlu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Natural Topology ◽  
Banach Contraction ◽  
Common Fixed Point Theorems

Recently, the concept of Ƒ metric space has been introduced and have been defined a natural topology in this spaces by Jleli and Samet[6]. Furthermore, a new style of Banach contraction principle has been given in the Ƒ metric spaces. In this paper, we prove some coincidence and common fixed point theorems in Ƒ metric spaces.

scholarly journals Some Fixed Point Results in Function Weighted Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Awais Asif ◽  
Nawab Hussain ◽  
Hamed Al-Sulami ◽  
Muahammad Arshad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Contractive Condition ◽  
Banach Contraction ◽  
The Banach Contraction Principle ◽  
Type Contraction ◽  
Unique Common Fixed Point

After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception of ℱ -metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting of ℱ -metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the whole ℱ -metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the whole ℱ -metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.

scholarly journals On Some New Results in Graphical Rectangular b-Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 488
Author(s):  
Pravin Baradol ◽  
Jelena Vujaković ◽  
Dhananjay Gopal ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we provide an approach to establish the Banach contraction principle ( for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).

scholarly journals Ordered-Theoretic Fixed Point Results in Fuzzy b-Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalil Javed ◽  
Fahim Uddin ◽  
Hassen Aydi ◽  
Aiman Mukheimer ◽  
Muhammad Arshad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Banach Contraction ◽  
Type Integral

The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric spaces and discuss some related fixed point results to ensure the existence and uniqueness of a fixed point. A nontrivial example is imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the provided results, an application is presented to solve the first kind of a Fredholm-type integral equation.

scholarly journals Existence and uniqueness of continuous solution of mixed type integra equations in cone metric space

1970 ◽  
Vol 7 (1) ◽  
pp. 48-55 ◽  
Author(s):  
HL Tidke ◽  
CT Aage ◽  
JN Salunke
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Fredholm Type ◽  
Type Integral ◽  
Banach’S Contraction Principle ◽  
Cone Metric

In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations in cone metric spaces. The result is obtained by using the some extensions of Banach's contraction principle in complete cone metric space. Mathematics Subject Classification: 45N05, 47G20, 34K05, 47H10. Keywords: Cone metric space, Contractive mapping, ordered Banach space. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5421 KUSET 2011; 7(1): 48-55

scholarly journals A New Kind of Nonlinear Quasicontractions in Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 661 ◽  
Author(s):  
Nicolae-Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Starting from two extensions of the Banach contraction principle due to Ćirić (1974) and Wardowski (2012), in the present paper we introduce the concepts of Ćirić type ψ F -contraction and ψ F -quasicontraction on a metric space and give some sufficient conditions under which the respective mappings are Picard operators. Some known fixed point results from the literature can be obtained as particular cases.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

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.

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