Symmetry in Metric Spaces and Topology

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 6479

Special Issue Editors


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Guest Editor
Young Researchers and Elite Club, West Tehran Branch, Islamic Azad University, Tehran 1477893855, Iran
Interests: analysis on metric spaces; operator theory; topology; fixed point theory and applications
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Guest Editor
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd 35, Serbia
Interests: nonlinear analysis; fixed point theory; operator theory
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Guest Editor
Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: general topology; fixed point theory; fuzzy metric spaces and related structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Analyzing metric spaces and topologies has been popular since the nineteenth century and has played a significant role in both classic and modern investigations for many years. New concepts (such as different metric spaces and distances) have been introduced up until this point. Moreover, topologists have worked on the convergency analysis of metric spaces and have identified the relationship between spaces, revealing that when various metric spaces coincide with topological concepts, they attract researchers studying applications and engineering principles. Furthermore, geometric analysis has many applications in the sciences, and when it comes to this branch of analysis, everyone thinks of the different metrics. Furthermore, many new definitions in various metric spaces regarding classical and modern analysis have been discussed over the past several years, and they have especially found many applications since 1908. The main purpose of this Special Issue is to state important developments in various metric spaces, with an emphasis on symmetric and asymmetric concepts. Thus, the Guest Editors want to invite researchers to send their high-quality papers on metric spaces, topologies, and symmetric concepts. We encourage you to contribute to the Special Issue “Symmetry in Metric Spaces and Topology”.

Dr. Ghasem Soleimani Rad
Prof. Dr. Stojan Radenovic
Prof. Dr. Salvador Romaguera
Guest Editors

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Keywords

  • various metric spaces
  • convergency and completeness of different metric spaces
  • metric spaces and symmetric and asymmetric properties
  • different distances and characterizations of various metric spaces
  • geometric analysis of metric spaces regarding ODEs and PDEs
  • various abstract metric spaces using Banach algebra and C*-algebra
  • topologically fixed point theories, symmetries, and asymmetries
  • applications of fixed point theory regarding spaces
  • metric-based and distance concepts and combinatorics (and the emphasis on graphs)
  • various metric spaces and fuzzy analysis
  • various metric spaces as new tools for artificial intelligence

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Published Papers (6 papers)

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Research

17 pages, 2711 KiB  
Article
Exact Solutions to the Oberbeck–Boussinesq Equations for Describing Three-Dimensional Flows of Micropolar Liquids
by Evgenii S. Baranovskii, Sergey V. Ershkov, Evgenii Yu. Prosviryakov and Alexander V. Yudin
Symmetry 2024, 16(12), 1669; https://doi.org/10.3390/sym16121669 - 17 Dec 2024
Viewed by 542
Abstract
The article proposes several classes of exact solutions to the Oberbeck–Boussinesq equations to describe convective flows of micropolar fluids. The possibility of using families of exact solutions for convective flows of classical incompressible fluids to micropolar incompressible fluids is discussed. It is shown [...] Read more.
The article proposes several classes of exact solutions to the Oberbeck–Boussinesq equations to describe convective flows of micropolar fluids. The possibility of using families of exact solutions for convective flows of classical incompressible fluids to micropolar incompressible fluids is discussed. It is shown that the three-dimensional Oberbeck–Boussinesq equation for describing steady and unsteady flows of micropolar fluids satisfies the class of Lin–Sidorov–Aristov exact solutions. The Lin–Sidorov–Aristov ansatz is characterized by a velocity field with a linear dependence on two spatial coordinates. These coordinates are called horizontal or longitudinal. The coefficients of the linear forms of the velocity field depend on the third coordinate (vertical or transverse) and time. The pressure field and the temperature field are described using quadratic forms. Generalizations of the Ostroumov–Birikh class are considered a special case of the Lin–Sidorov–Aristov family for describing unidirectional flows and homogeneous shear flows. An overdetermined system of Oberbeck–Boussinesq equations is investigated for describing non-homogeneous shear flows of non-trivial complex topology in 3D metric space. A compatibility condition is obtained in the Lin–Sidorov–Aristov class. Finally, a class of exact solutions with a vector velocity field that is nonlinear in part of the coordinates is presented in our analysis; such partially invariant solutions correspond to theoretical findings regarding symmetric/asymmetric properties of flow fields in solutions topology in a part of the existence appropriate for symmetry for the obtained invariant solutions. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
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18 pages, 285 KiB  
Article
Chen-like Inequalities for Submanifolds in Kähler Manifolds Admitting Semi-Symmetric Non-Metric Connections
by Ion Mihai and Andreea Olteanu
Symmetry 2024, 16(10), 1401; https://doi.org/10.3390/sym16101401 - 21 Oct 2024
Viewed by 1040
Abstract
The geometry of submanifolds in Kähler manifolds is an important research topic. In the present paper, we study submanifolds in complex space forms admitting a semi-symmetric non-metric connection. We prove the Chen–Ricci inequality, Chen basic inequality, and a generalized Euler inequality for such [...] Read more.
The geometry of submanifolds in Kähler manifolds is an important research topic. In the present paper, we study submanifolds in complex space forms admitting a semi-symmetric non-metric connection. We prove the Chen–Ricci inequality, Chen basic inequality, and a generalized Euler inequality for such submanifolds. These inequalities provide estimations of the mean curvature (the main extrinsic invariants) in terms of intrinsic invariants: Ricci curvature, the Chen invariant, and scalar curvature. In the proofs, we use the sectional curvature of a semi-symmetric, non-metric connection recently defined by A. Mihai and the first author, as well as its properties. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
12 pages, 279 KiB  
Article
On Modular b-Metrics
by Salvador Romaguera
Symmetry 2024, 16(10), 1333; https://doi.org/10.3390/sym16101333 - 9 Oct 2024
Viewed by 1160
Abstract
The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized [...] Read more.
The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized forms of Banach’s contraction principle for this new class of spaces thus initiating the study of the fixed point theory for these structures, where other authors have also made extensive contributions. In this paper we endow the modular b-metrics with a metrizable topology that supplies a firm endorsement of the idea of convergence proposed by Ege and Alaca in their article. Moreover, for a large class of modular b-metric spaces, we formulate this topology in terms of an explicitly defined b-metric, which extends both an important metrization theorem due to Chistyakov as well as the so-called topology of metric convergence. This approach allows us to characterize the completeness for this class of modular b-metric spaces that may be viewed as an offsetting of the celebrated Caristi–Kirk theorem to our context. We also include some examples that endorse our results. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
19 pages, 378 KiB  
Article
Solving Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions Using Covariant JS-Contractions
by Nawab Hussain, Nawal Alharbi and Ghada Basendwah
Symmetry 2024, 16(8), 939; https://doi.org/10.3390/sym16080939 - 23 Jul 2024
Cited by 1 | Viewed by 1111
Abstract
This paper investigates the existence, uniqueness, and symmetry of solutions for Φ–Atangana–Baleanu fractional differential equations of order μ(1,2] under mixed nonlocal boundary conditions. This is achieved through the use of covariant and contravariant JS-contractions [...] Read more.
This paper investigates the existence, uniqueness, and symmetry of solutions for Φ–Atangana–Baleanu fractional differential equations of order μ(1,2] under mixed nonlocal boundary conditions. This is achieved through the use of covariant and contravariant JS-contractions within a generalized framework of a sequential extended bipolar parametric metric space. As a consequence, we obtain the results on covariant and contravariant Ćirić, Chatterjea, Kannan, and Reich contractions as corollaries. Additionally, we substantiate our fixed-point findings with specific examples and derive similar results in the setting of sequential extended fuzzy bipolar metric space. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
14 pages, 297 KiB  
Article
A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions
by Kastriot Zoto, Vesna Šešum-Čavić, Mirjana Pantović, Vesna Todorčević, Marsela Zoto and Stojan Radenović
Symmetry 2024, 16(6), 739; https://doi.org/10.3390/sym16060739 - 13 Jun 2024
Cited by 1 | Viewed by 737
Abstract
This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness [...] Read more.
This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
16 pages, 291 KiB  
Article
Best Proximity Point Results via Simulation Function with Application to Fuzzy Fractional Differential Equations
by Ghada Ali, Nawab Hussain and Abdelhamid Moussaoui
Symmetry 2024, 16(5), 627; https://doi.org/10.3390/sym16050627 - 17 May 2024
Viewed by 859
Abstract
In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for [...] Read more.
In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
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