Special Issue "Abstract Metric Spaces: Usefulness in Statistics and Fixed Point Theory"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Set Theory".

Deadline for manuscript submissions: 20 December 2020.

Special Issue Editor

Prof. Dr. Antonio Francisco Roldán López de Hierro
Website
Guest Editor
Department of Statistics and Operations Research, University of Granada, Avda. del Hospicio, 18071 Granada, Spain
Interests: fuzzy numbers; fuzzy decision making; fuzzy regression; aggregation functions; fixed point theory
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Four properties characterize the notion of “metric”: non-negativity, identity of indiscernibles, symmetry, and triangle inequality (which is, maybe, the most important inequality in Mathematics). By combining the power of these four axioms, many possible applications have been created in several fields of study, especially in Mathematics and Physics. After the pioneering works of Fréchet (1906) and Hausdorff (1914), a great variety of modifications of the original notion have been introduced in order to extend and adapt this definition to each respective researcher’s interest area: semimetrics, quasimetrics, pseudometrics, partial metric spaces, Branciari distances, RS-distances, G-metric spaces, etc.

Taking into account convergent and Cauchy sequences in metric spaces, it is well known that the notion of “metric” plays a key role in fixed point theory. However, such a concept is also essential in Statistics, because it can model natural random phenomena better than other algebraic tools. Thus, statistical metric spaces, Menger spaces, fuzzy metric spaces, intuitionistic metric spaces, etc. have been introduced. Furthermore, in regression analysis, errors are computed using some generalized metrics in order to compare observed and theoretical points.

This Special Issue is devoted (but not limited) to the wide range of applications of the notion of “metric” in all fields of study, including topics such as:

  • Fixed point theory;
  • Fuzzy distances;
  • Generalized distances in abstract metrics spaces;
  • Applications of metrics in Statistics;
  • Use of metrics in regression analysis;
  • Convergence analysis;
  • Metrics in Computer Science.

Prof. Dr. Antonio Francisco Roldán López de Hierro
Guest Editor

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 papers will be 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 monthly 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 1200 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.

Published Papers (5 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Open AccessArticle
On ℋ-Simulation Functions and Fixed Point Results in the Setting of ωt-Distance Mappings with Application on Matrix Equations
Mathematics 2020, 8(5), 837; https://doi.org/10.3390/math8050837 - 21 May 2020
Abstract
The concepts of b-metric spaces and ω t -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We [...] Read more.
The concepts of b-metric spaces and ω t -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We introduce a new kind of function namely, H -simulation function which is used in this manuscript together with the notion of ω t -distance mappings to furnish for new contractions. Many fixed point results are proved based on these new contractions as well as some examples are introduced. Moreover, we introduce an application on matrix equations to focus on the importance of our work. Full article
Open AccessArticle
Cone Metric Spaces over Topological Modules and Fixed Point Theorems for Lipschitz Mappings
Mathematics 2020, 8(5), 724; https://doi.org/10.3390/math8050724 - 04 May 2020
Abstract
In this paper, we introduce the concept of cone metric space over a topological left module and we establish some coincidence and common fixed point theorems for self-mappings satisfying a condition of Lipschitz type. The main results of this paper provide extensions as [...] Read more.
In this paper, we introduce the concept of cone metric space over a topological left module and we establish some coincidence and common fixed point theorems for self-mappings satisfying a condition of Lipschitz type. The main results of this paper provide extensions as well as substantial generalizations and improvements of several well known results in the recent literature. In addition, the paper contains an example which shows that our main results are applicable on a non-metrizable cone metric space over a topological left module. The article proves that fixed point theorems in the framework of cone metric spaces over a topological left module are more effective and more fertile than standard results presented in cone metric spaces over a Banach algebra. Full article
Open AccessArticle
On Some New Multivalued Results in the Metric Spaces of Perov’s Type
Mathematics 2020, 8(3), 438; https://doi.org/10.3390/math8030438 - 17 Mar 2020
Abstract
The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov’s sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem [...] Read more.
The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov’s sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied. Full article
Open AccessArticle
Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces
Mathematics 2020, 8(3), 404; https://doi.org/10.3390/math8030404 - 12 Mar 2020
Abstract
The introduction of the common limit range property on V -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on V -fuzzy metric spaces. More precisely, we introduce the notion [...] Read more.
The introduction of the common limit range property on V -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on V -fuzzy metric spaces. More precisely, we introduce the notion of C L R Ω -property for the mappings Θ : M × M M and Ω : M M . We utilize our new notion to present and prove our new fixed point results. Full article
Open AccessArticle
A Result on a Pata-Ćirić Type Contraction at a Point
Mathematics 2020, 8(3), 393; https://doi.org/10.3390/math8030393 - 10 Mar 2020
Abstract
In this manuscript, we define a new contraction mapping, Pata-Ćirić type contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ćirić. We proved that in a complete space, each Pata-Ćirić type contraction at a point possesses a fixed point. [...] Read more.
In this manuscript, we define a new contraction mapping, Pata-Ćirić type contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ćirić. We proved that in a complete space, each Pata-Ćirić type contraction at a point possesses a fixed point. We express an example to illustrate the observed result. Full article
Back to TopTop