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Symmetry
Special Issues
Symmetry and Asymmetry in Fixed Point Theory and Computational Analysis
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Symmetry and Asymmetry in Fixed Point Theory and Computational Analysis

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 4999

Special Issue Editors

Prof. Dr. Wei-Shih Du

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Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Alicia Cordero

E-Mail Website
Guest Editor
School of Telecommunications Engineering, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: numerical analysis; iterative methods; nonlinear problems; discrete dynamics; real and complex
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Huaping Huang

E-Mail Website
Guest Editor
1. School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China
2. Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Interests: nonlinear functional analysis; complex analysis and differential equation theory; theory of fixed point in metric spaces and abstract metric spaces
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Juan Ramón Torregrosa Sánchez

E-Mail Website
Guest Editor
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Interests: iterative processes; matrix analysis; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over more than eight decades, the fascinating fixed point theory has increased the importance of contribution to improve our understanding of the real world around us in various fields about symmetry and asymmetry, such as linear and nonlinear analysis, symmetric and asymmetric optimization, differential equations and inclusions, economics, game theory, dynamic system theory, signal and image processing, and so forth. Over the last half a century, rapid developments in computational analysis and its applications have contributed greatly to immunological systems, computational systems, electrical and mechanical structures, financial markets, information and knowledge management, highway transportation networks, telecommunication networks and so on.

This Special Issue will pay more attention to the new originality of fixed point theory and computational analysis and their applications in integrating basic science into the real world, covering the widest range of symmetry and asymmetry. We cordially and earnestly invite researchers to contribute their original and high-quality research papers which will inspire advances in fixed point theory, computational analysis and their applications. Potential topics include, but are not limited to:

  • Symmetry and asymmetry in fixed point theory with applications
  • Symmetry and asymmetry in best proximity point theory with applications
  • Symmetry and asymmetry in numerical algorithms
  • Symmetry and asymmetry in nonlinear differential and integral equations
  • Symmetric and asymmetric optimization
  • Symmetry and asymmetry in nonlinear dynamical systems
  • Symmetry and asymmetry in image and signal processing
  • Symmetry and asymmetry in numerical analysis
  • Symmetry and asymmetry in computational geometry
  • Symmetry and asymmetry in computer graphics
  • Matrix theory
  • Visualization
  • Finite element method
  • Intelligence computation
  • Scientific and engineering computing
  • Data mining

Prof. Dr. Wei-Shih Du
Prof. Dr. Alicia Cordero Barbero
Prof. Dr. Huaping Huang
Prof. Dr. Juan Ramón Torregrosa Sánchez
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

  • Symmetry and asymmetry in fixed point theory
  • Symmetry and asymmetry in best proximity point theory
  • Symmetry and asymmetry in algorithms
  • Symmetry and asymmetry in optimization
  • Symmetry and asymmetry in dynamical systems
  • Symmetry and asymmetry in numerical analysis
  • Symmetry and asymmetry in image and signal processing
  • Matrix theory
  • Visualization
  • Intelligence computation
  • Data mining

Published Papers (4 papers)

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Research

20 pages, 583 KiB  
Article
New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction
by Alicia Cordero, Smmayya Iqbal, Juan R. Torregrosa and Fiza Zafar
Symmetry 2022, 14(8), 1742; https://doi.org/10.3390/sym14081742 - 22 Aug 2022
Cited by 1 | Viewed by 1327
Abstract
We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are [...] Read more.
We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are analyzed, showing their symmetric wide sets of converging initial guesses. To illustrate the applicability of our methods for the multidimensional case, we choose some real world problems such as kinematic syntheses, boundary value problems, Fisher’s and Hammerstein’s integrals, etc. Numerical comparisons are given to show the performance of our schemes, compared with the existing efficient methods. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Fixed Point Theory and Computational Analysis)
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23 pages, 362 KiB  
Article
Coupled Fixed Point Theorems with Rational Type Contractive Condition via C-Class Functions and Inverse Ck-Class Functions
by Xiaolan Liu, Mi Zhou, Arslan H. Ansari, Kalyan Chakrabarti, Mujahid Abbas and Laxmi Rathour
Symmetry 2022, 14(8), 1663; https://doi.org/10.3390/sym14081663 - 11 Aug 2022
Cited by 1 | Viewed by 1414
Abstract
The purpose of this paper is to develop coupled fixed point theorems by C-class functions with mixed monotonicity, discuss the existence of the coupled fixed point of two mappings and obtain a coupled coincidence point theorem via inverse Ck-class functions [...] Read more.
The purpose of this paper is to develop coupled fixed point theorems by C-class functions with mixed monotonicity, discuss the existence of the coupled fixed point of two mappings and obtain a coupled coincidence point theorem via inverse Ck-class functions in partially ordered H-metric spaces. This improves the existing results. In addition, some instances and an application are given to illustrate the usability and validity of the results. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Fixed Point Theory and Computational Analysis)
17 pages, 525 KiB  
Article
A Regularized Generalized Popov’s Method to Solve the Hierarchical Variational Inequality Problem with Generalized Lipschitzian Mappings
by Yuanheng Wang, Yidan Gao and Bingnan Jiang
Symmetry 2022, 14(2), 187; https://doi.org/10.3390/sym14020187 - 18 Jan 2022
Cited by 2 | Viewed by 1040
Abstract
In this article, we introduce a new inertial multi-step regularized generalized Popov’s extra-gradient method to solve the hierarchical variational inequality problem (HVIP). We extend the previous Lipschitzian and strongly monotone mapping to a hemicontinuous, generalized Lipschitzian and strongly monotone mapping. We also obtain [...] Read more.
In this article, we introduce a new inertial multi-step regularized generalized Popov’s extra-gradient method to solve the hierarchical variational inequality problem (HVIP). We extend the previous Lipschitzian and strongly monotone mapping to a hemicontinuous, generalized Lipschitzian and strongly monotone mapping. We also obtain a strong convergence theorem about the new Popov’s algorithm. Furthermore, we utilize some numerical experiments to highlight the feasibility and effectiveness of our method. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Fixed Point Theory and Computational Analysis)
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16 pages, 328 KiB  
Article
On the Unique Solvability of Incomplete Cauchy Type Problems for a Class of Multi-Term Equations with the Riemann–Liouville Derivatives
by Vladimir E. Fedorov, Wei-Shih Du and Mikhail M. Turov
Symmetry 2022, 14(1), 75; https://doi.org/10.3390/sym14010075 - 05 Jan 2022
Cited by 12 | Viewed by 1316
Abstract
Incomplete Cauchy-type problems are considered for linear multi-term equations solved with respect to the highest derivative in Banach spaces with fractional Riemann–Liouville derivatives and with linear closed operators at them. Some new existence and uniqueness theorems for solutions are presented explicitly and the [...] Read more.
Incomplete Cauchy-type problems are considered for linear multi-term equations solved with respect to the highest derivative in Banach spaces with fractional Riemann–Liouville derivatives and with linear closed operators at them. Some new existence and uniqueness theorems for solutions are presented explicitly and the analyticity of the solutions of the homogeneous equations are also shown. The asymmetry of the Cauchy-type problem under study is expressed in the presence of a so-called defect, which shows the number of lower-order initial conditions that should not be set when setting the problem. As applications, our abstract results are used in the study of a class of initial-boundary value problems for multi-term equations with Riemann–Liouville derivatives in time and with polynomials of a self-adjoint elliptic differential operator with respect to spatial variables. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Fixed Point Theory and Computational Analysis)
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