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Symmetry
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Symmetry in Nonlinear Functional Analysis and Optimization Theory II
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Symmetry in Nonlinear Functional Analysis and Optimization Theory II

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

Deadline for manuscript submissions: closed (15 March 2023) | Viewed by 10311

Special Issue Editors

Dr. Yagub Sharifov

E-Mail Website
Guest Editor
Institute of Cybernetics, ANAS, and Baku State University, 1141 Baku, Azerbaijan
Interests: fractional differential equations; nonlocal boundary conditins; existence and uniqueness solutions; solvobality
Prof. Dr. Nazim Mahmudov

E-Mail Website
Guest Editor
Department of Mathematics, Eastern Mediterranean University, Gazimagusa 99628, TRNC, via Mersin 10, Turkey
Interests: fractional deterministic and stochastic differential/difference equations; stochastic calculus; fractional calculus; stability analysis; control theory; numerical methods for fractional differential equations, discrete fractional calculus
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear Functional Analysis and Optimization Theory are two closed related two research fields in applied mathematics. A lot of problems such as differential equations and integral equations in nonlinear analysis, can be solved via optimization methods. In particular, fixed/zero-point problems nonlinear operators are under the spotlight of mathematicians working on optimization theory. Recently, a number of optimization methods, such as, projection-like methods, have been investigated for solving various nonlinear equations. Many important applications have been carried out in engineering fields, such as, transportation, economics, medicine, and machine learning.

In this Special Issue, we will focus on high-quality research on nonlinear functional analysis and optimization theory, in particular complementary problems, differential equation, integral equations, equilibrium problems, monotone operators, fixed/zero points, convex feasibility problems, split feasibility problems and their applications to the real world.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Dr. Yagub Sharifov
Prof. Dr. Nazim Mahmudov
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

  • complementary problems
  • differential equation
  • equilibrium problems
  • monotone operators
  • convex feasibility problems
  • split feasibility problems
  • machine learning

Published Papers (7 papers)

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Research

27 pages, 437 KiB  
Article
A Class of Sparse Direct Broyden Method for Solving Sparse Nonlinear Equations
by Huiping Cao and Jing Han
Symmetry 2022, 14(8), 1552; https://doi.org/10.3390/sym14081552 - 28 Jul 2022
Viewed by 1355
Abstract
In our paper, we present a sparse quasi-Newton method, called the sparse direct Broyden method, for solving sparse nonlinear equations. The method can be seen as a Broyden-like method and is a least change update satisfying the sparsity condition and direct tangent condition [...] Read more.
In our paper, we present a sparse quasi-Newton method, called the sparse direct Broyden method, for solving sparse nonlinear equations. The method can be seen as a Broyden-like method and is a least change update satisfying the sparsity condition and direct tangent condition simultaneously. The local and q-superlinear convergence is presented based on the bounded deterioration property and Dennis–Moré condition. By adopting a nonmonotone line search, we establish the global and superlinear convergence. Moreover, the unit step length is essentially accepted. Numerical results demonstrate that the sparse direct Broyden method is effective and competitive for large-scale nonlinear equations. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
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17 pages, 312 KiB  
Article
Characterizations of Well-Posedness for Generalized Hemivariational Inequalities Systems with Derived Inclusion Problems Systems in Banach Spaces
by Lu-Chuan Ceng, Jian-Ye Li, Cong-Shan Wang, Fang-Fei Zhang, Hui-Ying Hu, Yun-Ling Cui and Long He
Symmetry 2022, 14(7), 1341; https://doi.org/10.3390/sym14071341 - 29 Jun 2022
Viewed by 1073
Abstract
In real Banach spaces, the concept of α-well-posedness is extended to the class of generalized hemivariational inequalities systems consisting of two parts which are of symmetric structure mutually. First, certain concepts of α-well-posedness for generalized hemivariational inequalities systems are put forward. [...] Read more.
In real Banach spaces, the concept of α-well-posedness is extended to the class of generalized hemivariational inequalities systems consisting of two parts which are of symmetric structure mutually. First, certain concepts of α-well-posedness for generalized hemivariational inequalities systems are put forward. Second, certain metric characterizations of α-well-posedness for generalized hemivariational inequalities systems are presented. Lastly, certain equivalence results between strong α-well-posedness of both the system of generalized hemivariational inequalities and its system of derived inclusion problems are established. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
13 pages, 342 KiB  
Article
Kantorovich Type Generalization of Bernstein Type Rational Functions Based on (p,q)-Integers
by Hayatem Hamal and Pembe Sabancigil
Symmetry 2022, 14(5), 1054; https://doi.org/10.3390/sym14051054 - 20 May 2022
Cited by 1 | Viewed by 1130
Abstract
In this paper, we define a new Kantorovich-type (p,q)-generalization of the Balázs–Szabados operators. We derive a recurrence formula, and with the help of this formula, we give explicit formulas for the first and second-order moments, which follow a [...] Read more.
In this paper, we define a new Kantorovich-type (p,q)-generalization of the Balázs–Szabados operators. We derive a recurrence formula, and with the help of this formula, we give explicit formulas for the first and second-order moments, which follow a symmetric pattern. We estimate the second and fourth-order central moments. We examine the local approximation properties in terms of modulus of continuity, we give a Voronovskaja type theorem, and we give the weighted approximation properties of the operators. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
12 pages, 805 KiB  
Article
Global Well-Posedness and Analyticity of the Primitive Equations of Geophysics in Variable Exponent Fourier–Besov Spaces
by Muhammad Zainul Abidin, Naeem Ullah and Omer Abdalrhman Omer
Symmetry 2022, 14(1), 165; https://doi.org/10.3390/sym14010165 - 14 Jan 2022
Cited by 2 | Viewed by 1508
Abstract
We consider the Cauchy problem of the three-dimensional primitive equations of geophysics. By using the Littlewood–Paley decomposition theory and Fourier localization technique, we prove the global well-posedness for the Cauchy problem with the Prandtl number P=1 in variable exponent Fourier–Besov spaces [...] Read more.
We consider the Cauchy problem of the three-dimensional primitive equations of geophysics. By using the Littlewood–Paley decomposition theory and Fourier localization technique, we prove the global well-posedness for the Cauchy problem with the Prandtl number P=1 in variable exponent Fourier–Besov spaces for small initial data in these spaces. In addition, we prove the Gevrey class regularity of the solution. For the primitive equations of geophysics, our results can be considered as a symmetry in variable exponent Fourier–Besov spaces. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
14 pages, 295 KiB  
Article
Using Rough Set Theory to Find Minimal Log with Rule Generation
by Tahani Nawaf Alawneh and Mehmet Ali Tut
Symmetry 2021, 13(10), 1906; https://doi.org/10.3390/sym13101906 - 10 Oct 2021
Cited by 1 | Viewed by 1340
Abstract
Data pre-processing is a major difficulty in the knowledge discovery process, especially feature selection on a large amount of data. In literature, various approaches have been suggested to overcome this difficulty. Unlike most approaches, Rough Set Theory (RST) can discover data de-pendency and [...] Read more.
Data pre-processing is a major difficulty in the knowledge discovery process, especially feature selection on a large amount of data. In literature, various approaches have been suggested to overcome this difficulty. Unlike most approaches, Rough Set Theory (RST) can discover data de-pendency and reduce the attributes without the need for further information. In RST, the discernibility matrix is the mathematical foundation for computing such reducts. Although it proved its efficiency in feature selection, unfortunately it is computationally expensive on high dimensional data. Algorithm complexity is related to the search of the minimal subset of attributes, which requires computing an exponential number of possible subsets. To overcome this limitation, many RST enhancements have been proposed. Contrary to recent methods, this paper implements RST concepts in an iterated manner using R language. First, the dataset was partitioned into a smaller number of subsets and each subset processed independently to generate its own minimal attribute set. Within the iterations, only minimal elements in the discernibility matrix were considered. Finally, the iterated outputs were compared, and those common among all reducts formed the minimal one (Core attributes). A comparison with another novel proposed algorithm using three benchmark datasets was performed. The proposed approach showed its efficiency in calculating the same minimal attribute sets with less execution time. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
18 pages, 318 KiB  
Article
On the Parallel Subgradient Extragradient Rule for Solving Systems of Variational Inequalities in Hadamard Manifolds
by Chun-Yan Wang, Lu-Chuan Ceng, Long He, Hui-Ying Hu, Tu-Yan Zhao, Dan-Qiong Wang and Hong-Ling Fan
Symmetry 2021, 13(8), 1496; https://doi.org/10.3390/sym13081496 - 15 Aug 2021
Cited by 1 | Viewed by 1321
Abstract
In a Hadamard manifold, let the VIP and SVI represent a variational inequality problem and a system of variational inequalities, respectively, where the SVI consists of two variational inequalities which are of symmetric structure mutually. This article designs two parallel algorithms to solve [...] Read more.
In a Hadamard manifold, let the VIP and SVI represent a variational inequality problem and a system of variational inequalities, respectively, where the SVI consists of two variational inequalities which are of symmetric structure mutually. This article designs two parallel algorithms to solve the SVI via the subgradient extragradient approach, where each algorithm consists of two parts which are of symmetric structure mutually. It is proven that, if the underlying vector fields are of monotonicity, then the sequences constructed by these algorithms converge to a solution of the SVI. We also discuss applications of these algorithms for approximating solutions to the VIP. Our theorems complement some recent and important ones in the literature. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
13 pages, 254 KiB  
Article
Refinements of Wilker–Huygens-Type Inequalities via Trigonometric Series
by Gabriel Bercu
Symmetry 2021, 13(8), 1323; https://doi.org/10.3390/sym13081323 - 22 Jul 2021
Viewed by 1144
Abstract
The study of even functions is important from the symmetry theory point of view because their graphs are symmetrical to the Oy axis; therefore, it is essential to analyse the properties of even functions for x greater than 0. Since the functions [...] Read more.
The study of even functions is important from the symmetry theory point of view because their graphs are symmetrical to the Oy axis; therefore, it is essential to analyse the properties of even functions for x greater than 0. Since the functions involved in Wilker–Huygens-type inequalities are even, in our approach, we use cosine polynomials expansion method in order to provide new refinements of the above-mentioned inequalities. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
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