Symmetry in Geometry and Topology: Theory and Application

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 1955

Special Issue Editors


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Guest Editor
Department of Mathematics, Fırat University, 23119 Elazığ, Turkey
Interests: sequence spaces; fuzzy sequences; dual spaces; statistical convergence; geometrics properties

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Guest Editor
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
Interests: sequence spaces; application of fixed point theory; measure of non-compactness; fractional calculus; nonlinear analysis
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Guest Editor
Department of Mathematics and Computer Sciences, University of Prishtina Avenue Mother Teresa, Nr=5, 10000 Prishtine, Kosovo
Interests: functional analysis

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Guest Editor
Department of Mathematics, Universidad de Cádiz, Apdo. 40, 11510 Puerto Real, Spain
Interests: functional analysis
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Guest Editor
Institute of Mathematics and Applications, Bhubaneswar 751029, Odisha, India
Interests: sequence spaces; difference operators; fractional derivatives

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to focus on recent developments and achievements in functional analysis such as the topology and symmetry of Banach spaces and their geometry, statistical summability, and statistical approximation, almost summability, fuzzy sequence spaces, matrix summability, compact matrix operators between sequence spaces and infinite systems of differential and integral equations in sequence spaces, and various applications. We cordially invite researchers to submit original research and review articles describing new methods and applications that are directly or indirectly related to summability, function spaces, and sequence spaces. We also welcome research including fixed-point theory, operator theory, approximation theory, and symmetry. Potential topics include, but are not limited to, the following:

  • The geometry, topology, and symmetry of sequence spaces;
  • Polynomials and positive operators and symmetry;
  • Summability methods for q-operators and symmetry;
  • Approximation and statistical approximation with applications in computer-aided design and optimization, and symmetry;
  • Fixed point theory and applications;
  • Matrix and non-matrix methods, associated compact operators, and symmetry;
  • Dual summability methods associated with symmetry;
  • Classical sequence spaces and their matrix domains associated with symmetry;
  • Different sequence spaces and their applications;
  • Statistical convergence in probability, Riesz spaces, and normed spaces;
  • Fuzzy sequence spaces;
  • Symmetric sequence spaces.

Prof. Dr. Mikâil Et
Prof. Dr. Bipan Hazarika
Prof. Dr. Naim L. Braha
Dr. María C. Listán-García
Dr. Pinakadhar Baliarsingh
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. Symmetry 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 2400 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

  • asymptotically statistically equivalence
  • difference sequence
  • fractional operator
  • statistical convergence
  • fuzzy sequence space
  • symmetric sequence space
  • Szász–Mirakyan operators
  • matrix methods
  • modulus function
  • Voronovskaja theorem
  • Korovkin-type theorem
  • fixed point theory
  • nonexpansive mappings
  • q-calculus
  • quantum difference operator
  • α-, β-, and γ-duals
  • point spectrum
  • continuous spectrum
  • residual spectrum
  • statistical convergence in probability

Published Papers (2 papers)

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Research

16 pages, 357 KiB  
Article
On Some Sequence Spaces via q-Pascal Matrix and Its Geometric Properties
by Taja Yaying, Bipan Hazarika and Mikail Et
Symmetry 2023, 15(9), 1659; https://doi.org/10.3390/sym15091659 - 28 Aug 2023
Viewed by 568
Abstract
We develop some new sequence spaces 𝓁p(P(q)) and 𝓁(P(q)) by using q-Pascal matrix P(q). We discuss some topological properties of the newly defined spaces, [...] Read more.
We develop some new sequence spaces 𝓁p(P(q)) and 𝓁(P(q)) by using q-Pascal matrix P(q). We discuss some topological properties of the newly defined spaces, obtain the Schauder basis for the space 𝓁p(P(q)) and determine the Alpha-(α-), Beta-(β-) and Gamma-(γ-) duals of the newly defined spaces. We characterize a certain class (𝓁p(P(q)),X) of infinite matrices, where X{𝓁,c,c0}. Furthermore, utilizing the proposed results, we characterize certain other classes of infinite matrices. We also examine some geometric properties, like the approximation property, Dunford–Pettis property, Hahn–Banach extension property, and Banach–Saks-type p property of the spaces 𝓁p(P(q)) and 𝓁(P(q)). Full article
(This article belongs to the Special Issue Symmetry in Geometry and Topology: Theory and Application)
12 pages, 281 KiB  
Article
On Some Topological and Geometric Properties of Some q-Cesáro Sequence Spaces
by Yılmaz Yılmaz and Ahmet Ocak Akdemir
Symmetry 2023, 15(4), 791; https://doi.org/10.3390/sym15040791 - 24 Mar 2023
Cited by 1 | Viewed by 803
Abstract
Mathematical concepts are aesthetic tools that are useful to create methods or solutions to real-world problems in theory and practice, and that sometimes contain symmetrical and asymmetrical structures due to the nature of the problems. In this study, we investigate whether the sequence [...] Read more.
Mathematical concepts are aesthetic tools that are useful to create methods or solutions to real-world problems in theory and practice, and that sometimes contain symmetrical and asymmetrical structures due to the nature of the problems. In this study, we investigate whether the sequence spaces Xpq, 0p<, and X, which are constructed by q-Cesáro matrix, satisfy some of the further properties described with respect to the bounded linear operators on them. More specifically, we answer to the question: “Which of these spaces have the Approximation, Dunford-Pettis, Radon–Riesz and Hahn–Banach extension properties?”. Furthermore, we try to investigate some geometric properties such as rotundity and smootness of these spaces. Full article
(This article belongs to the Special Issue Symmetry in Geometry and Topology: Theory and Application)
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