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Mathematics
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Recent Advances on Quasi-Metric Spaces
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Recent Advances on Quasi-Metric Spaces

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (1 December 2019) | Viewed by 18367

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Andreea Fulga

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Guest Editor
Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, 500036 Brasov, Romania
Interests: mathematical analysis; operator theory; real analysis; functional analysis
Prof. Dr. Erdal Karapinar

E-Mail Website
Guest Editor
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Interests: functional analysis; operator theory; linear topological invariants; fixed point theory; best proximity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The quasi-metric, which is a natural generalization of the notion of the metric, has been one of the important topics in topology and analysis in the last few decades. Roughly speaking, the quasi-metric appears to be obtained by relaxing the symmetric condition from the axioms of the standard metric. Regarding physical phenomena, the quasi-metric can be more useful in solving real-life problems. On the other hand, one can question whether there is a positive constant D such that the distance from a point x to y is dominated by D times the distance from y to x. The answer is affirmative, and such spaces are called the D-symmetric quasi-metric. These spaces are quite rich since they lie between the quasi-metric spaces and metric spaces, and they have proven to be very interesting topics for researchers who work in fixed point theory.

Dr. Andreea Fulga
Prof. Erdal Karapinar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quasi-metric
  • DELTA-symmetric quasi metric
  • Fixed point
  • Best proximity point
  • Common fixed point
  • Interpolative contraction

Published Papers (8 papers)

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Research

10 pages, 276 KiB  
Article
A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation
by Watcharin Chartbupapan, Ovidiu Bagdasar and Kanit Mukdasai
Mathematics 2020, 8(1), 82; https://doi.org/10.3390/math8010082 - 03 Jan 2020
Cited by 23 | Viewed by 2110
Abstract
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, [...] Read more.
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
5 pages, 247 KiB  
Article
A Characterization of Quasi-Metric Completeness in Terms of α–ψ-Contractive Mappings Having Fixed Points
by Salvador Romaguera and Pedro Tirado
Mathematics 2020, 8(1), 16; https://doi.org/10.3390/math8010016 - 19 Dec 2019
Cited by 12 | Viewed by 1753
Abstract
We obtain a characterization of Hausdorff left K-complete quasi-metric spaces by means of α – ψ -contractive mappings, from which we deduce the somewhat surprising fact that one the main fixed point theorems of Samet, Vetro, and Vetro (see “Fixed point theorems for [...] Read more.
We obtain a characterization of Hausdorff left K-complete quasi-metric spaces by means of α – ψ -contractive mappings, from which we deduce the somewhat surprising fact that one the main fixed point theorems of Samet, Vetro, and Vetro (see “Fixed point theorems for α – ψ -contractive type mappings”, Nonlinear Anal. 2012, 75, 2154–2165), characterizes the metric completeness. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
23 pages, 373 KiB  
Article
Ample Spectrum Contractions and Related Fixed Point Theorems
by Antonio Francisco Roldán López de Hierro and Naseer Shahzad
Mathematics 2019, 7(11), 1033; https://doi.org/10.3390/math7111033 - 02 Nov 2019
Cited by 5 | Viewed by 1595
Abstract
Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, [...] Read more.
Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
14 pages, 246 KiB  
Article
Modified Suzuki-Simulation Type Contractive Mapping in Non-Archimedean Quasi Modular Metric Spaces and Application to Graph Theory
by Ekber Girgin and Mahpeyker Öztürk
Mathematics 2019, 7(9), 769; https://doi.org/10.3390/math7090769 - 21 Aug 2019
Cited by 1 | Viewed by 1961
Abstract
In this paper, we establish generalized Suzuki-simulation-type contractive mapping and prove fixed point theorems on non-Archimedean quasi modular metric spaces. As an application, we acquire graphic-type results. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
11 pages, 241 KiB  
Article
On Pata–Suzuki-Type Contractions
by Obaid Alqahtani, Venigalla Madhulatha Himabindu and Erdal Karapınar
Mathematics 2019, 7(8), 720; https://doi.org/10.3390/math7080720 - 08 Aug 2019
Cited by 10 | Viewed by 2248
Abstract
In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the [...] Read more.
In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
9 pages, 241 KiB  
Article
Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces
by Wasfi Shatanawi and Kamaleldin Abodayeh
Mathematics 2019, 7(5), 453; https://doi.org/10.3390/math7050453 - 20 May 2019
Cited by 5 | Viewed by 2034
Abstract
We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction. [...] Read more.
We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
14 pages, 263 KiB  
Article
Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application
by Pradip R. Patle, Deepesh Kumar Patel, Hassen Aydi, Dhananjay Gopal and Nabil Mlaiki
Mathematics 2019, 7(4), 373; https://doi.org/10.3390/math7040373 - 24 Apr 2019
Cited by 12 | Viewed by 2914
Abstract
This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent [...] Read more.
This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
4 pages, 204 KiB  
Article
A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces
by Erdal Karapınar, Farshid Khojasteh and Zoran D. Mitrović
Mathematics 2019, 7(4), 308; https://doi.org/10.3390/math7040308 - 27 Mar 2019
Cited by 26 | Viewed by 2808
Abstract
In this paper, we revisit the renowned fixed point theorems belongs to Caristi and Banach. We propose a new fixed point theorem which is inspired from both Caristi and Banach. We also consider an example to illustrate our result. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
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