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Symmetry
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Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry
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Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry

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

Deadline for manuscript submissions: closed (5 July 2022) | Viewed by 19097

Special Issue Editor

Prof. Dr. Eulalia Martínez Molada

E-Mail Website
Guest Editor
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Interests: numerical analysis; iterative methods in Banach spaces; semilocal and local convergence; computational efficiency
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Recently, fixed point theory (with topological fixed point theory, metric fixed point theory, and discrete fixed point theory), geometry of Banach spaces, and symmetry are very important and powerful tools to study nonlinear analysis and applications, especially nonlinear operator theory and applications, equilibrium problems and applications, variational inequality problems and applications, complementarity problems and applications, saddle point theory and applications, differential and integral equations and applications, optimization problems and applications, approximation theory and applications, numerical analysis and applications, the stability of functional equations, game theory and applications, programming problems and applications, engineering, topology, economics, geometry, inequality problems, and many others.

The aim of this Special Issue of Symmetry is to enhance the new development of fixed point theory, related nonlinear problems, the geometry of Banach spaces, and symmetry with applications. Our Guest Editor will accept very-high-quality papers containing original results and survey articles of exceptional merit. Due to the great success of our Special Issue "Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry" we decided to set up a second volume. We invite you to contribute to the Special Issue "Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry II" by https://www.mdpi.com/journal/symmetry/special_issues/J1V0TZBN20.

Prof. Dr. Eulalia Martínez Molada
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 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

  • fixed point theory and applications
  • best proximity point theory and applications
  • nonlinear operator theory and applications
  • generalized contractive mappings
  • equilibrium problems and applications
  • variational inequality problems and applications
  • optimization problems and applications
  • game theory and applications
  • numerical algorithms for nonlinear problems
  • well-posedness in fixed point theory
  • stability of functional equations related to fixed point theory
  • differential and integral equations
  • geometry of Banach spaces
  • symmetry

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Published Papers (10 papers)

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Research

16 pages, 323 KiB  
Article
Approximating Fixed Points of Relatively Nonexpansive Mappings via Thakur Iteration
by V. Pragadeeswarar, R. Gopi and M. De la Sen
Symmetry 2022, 14(6), 1107; https://doi.org/10.3390/sym14061107 - 27 May 2022
Viewed by 1483
Abstract
The study of symmetry is a major tool in the nonlinear analysis. The symmetricity of distance function in a metric space plays important role in proving the existence of a fixed point for a self mapping. In this work, we approximate a fixed [...] Read more.
The study of symmetry is a major tool in the nonlinear analysis. The symmetricity of distance function in a metric space plays important role in proving the existence of a fixed point for a self mapping. In this work, we approximate a fixed point of noncyclic relatively nonexpansive mappings by using a three-step Thakur iterative scheme in uniformly convex Banach spaces. We also provide a numerical example where the Thakur iterative scheme is faster than some well known iterative schemes such as Picard, Mann, and Ishikawa iteration. Finally, we provide a stronger version of our proposed theorem via von Neumann sequences. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
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18 pages, 406 KiB  
Article
A Subgradient-Type Extrapolation Cyclic Method for Solving an Equilibrium Problem over the Common Fixed-Point Sets
by Porntip Promsinchai and Nimit Nimana
Symmetry 2022, 14(5), 992; https://doi.org/10.3390/sym14050992 - 12 May 2022
Viewed by 1922
Abstract
In this paper, we consider the solving of an equilibrium problem over the common fixed set of cutter mappings in a real Hilbert space. To this end, we present a subgradient-type extrapolation cyclic method. The proposed method is generated based on the ideas [...] Read more.
In this paper, we consider the solving of an equilibrium problem over the common fixed set of cutter mappings in a real Hilbert space. To this end, we present a subgradient-type extrapolation cyclic method. The proposed method is generated based on the ideas of a subgradient method and an extrapolated cyclic cutter method. We prove a strong convergence of the method provided that some suitable assumptions of step-size sequences are assumed. We finally show the numerical behavior of the proposed method. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
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12 pages, 301 KiB  
Article
A Family of Derivative Free Algorithms for Multiple-Roots of Van Der Waals Problem
by Sunil Kumar, Ramandeep Behl, Eulalia Martínez, Fouad Mallawi and Sattam Alharbi
Symmetry 2022, 14(3), 562; https://doi.org/10.3390/sym14030562 - 11 Mar 2022
Cited by 1 | Viewed by 1707
Abstract
There are a good number of higher-order iterative methods for computing multiple zeros of nonlinear equations in the available literature. Most of them required first or higher-order derivatives of the involved function. No doubt, high-order derivative-free methods for multiple zeros are more difficult [...] Read more.
There are a good number of higher-order iterative methods for computing multiple zeros of nonlinear equations in the available literature. Most of them required first or higher-order derivatives of the involved function. No doubt, high-order derivative-free methods for multiple zeros are more difficult to obtain in comparison with simple zeros and with first order derivatives. This study presents an optimal family of fourth order derivative-free techniques for multiple zeros that requires just three evaluations of function ϕ, per iteration. The approximations of the derivative/s are based on symmetric divided differences. We also demonstrate the application of new algorithms on Van der Waals, Planck law radiation, Manning for isentropic supersonic flow and complex root problems. Numerical results reveal that the proposed derivative-free techniques are more efficient in comparison terms of CPU, residual error, computational order of convergence, number of iterations and the difference between two consecutive iterations with other existing methods. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
18 pages, 539 KiB  
Article
Symmetry in the Multidimensional Dynamical Analysis of Iterative Methods with Memory
by Alicia Cordero, Neus Garrido, Juan R. Torregrosa and Paula Triguero-Navarro
Symmetry 2022, 14(3), 442; https://doi.org/10.3390/sym14030442 - 23 Feb 2022
Viewed by 1475
Abstract
In this paper, new tools for the dynamical analysis of iterative schemes with memory for solving nonlinear systems of equations are proposed. These tools are in concordance with those of the scalar case and provide interesting results about the symmetry and wideness of [...] Read more.
In this paper, new tools for the dynamical analysis of iterative schemes with memory for solving nonlinear systems of equations are proposed. These tools are in concordance with those of the scalar case and provide interesting results about the symmetry and wideness of the basins of attraction on different iterative procedures with memory existing in the literature. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
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16 pages, 291 KiB  
Article
Some New James Type Geometric Constants in Banach Spaces
by Bingren Chen, Zhijian Yang, Qi Liu and Yongjin Li
Symmetry 2022, 14(2), 405; https://doi.org/10.3390/sym14020405 - 18 Feb 2022
Viewed by 1487
Abstract
We will introduce four new geometric constants closely related to the James constant J(X), which have symmetric structure, along with a discussion on the relationships among them and some other well-known geometric constants via several inequalities, together with the [...] Read more.
We will introduce four new geometric constants closely related to the James constant J(X), which have symmetric structure, along with a discussion on the relationships among them and some other well-known geometric constants via several inequalities, together with the calculation of several values on some specific spaces. In addition, we will characterize geometric properties of J1(X), such as uniform non-squareness and uniformly normal structure. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
22 pages, 1151 KiB  
Article
A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces
by Godwin Chidi Ugwunnadi, Lateef Olakunle Jolaoso and Chibueze Christian Okeke
Symmetry 2022, 14(2), 335; https://doi.org/10.3390/sym14020335 - 6 Feb 2022
Viewed by 1526
Abstract
In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general [...] Read more.
In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general mathematical problem in the sense that it unifies several mathematical models arising in (symmetry and non-symmetry) optimization theory and also finds many applications in applied science. We designed the algorithm in such a way that the convergence analysis does not need a prior estimate of the operator norm. More so, we establish the strong convergence of our algorithm and present some computational examples to illustrate the performance of the proposed method. In addition, we give an application of our result for solving the image restoration problem and compare with other algorithms in the literature. This result improves and generalizes many important related results in the contemporary literature. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
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26 pages, 1030 KiB  
Article
An Algorithm Derivative-Free to Improve the Steffensen-Type Methods
by Miguel A. Hernández-Verón, Sonia Yadav, Ángel Alberto Magreñán, Eulalia Martínez and Sukhjit Singh
Symmetry 2022, 14(1), 4; https://doi.org/10.3390/sym14010004 - 21 Dec 2021
Cited by 1 | Viewed by 2386
Abstract
Solving equations of the form H(x)=0 is one of the most faced problem in mathematics and in other science fields such as chemistry or physics. This kind of equations cannot be solved without the use of iterative methods. [...] Read more.
Solving equations of the form H(x)=0 is one of the most faced problem in mathematics and in other science fields such as chemistry or physics. This kind of equations cannot be solved without the use of iterative methods. The Steffensen-type methods, defined using divided differences are derivative free, are usually considered to solve these problems when H is a non-differentiable operator due to its accuracy and efficiency. However, in general, the accessibility of these iterative methods is small. The main interest of this paper is to improve the accessibility of Steffensen-type methods, this is the set of starting points that converge to the roots applying those methods. So, by means of using a predictor–corrector iterative process we can improve this accessibility. For this, we use a predictor iterative process, using symmetric divided differences, with good accessibility and then, as corrector method, we consider the Center-Steffensen method with quadratic convergence. In addition, the dynamical studies presented show, in an experimental way, that this iterative process also improves the region of accessibility of Steffensen-type methods. Moreover, we analyze the semilocal convergence of the predictor–corrector iterative process proposed in two cases: when H is differentiable and H is non-differentiable. Summing up, we present an effective alternative for Newton’s method to non-differentiable operators, where this method cannot be applied. The theoretical results are illustrated with numerical experiments. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
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13 pages, 272 KiB  
Article
Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds
by Jinhua Zhu, Jinfang Tang, Shih-sen Chang, Min Liu and Liangcai Zhao
Symmetry 2021, 13(7), 1161; https://doi.org/10.3390/sym13071161 - 28 Jun 2021
Cited by 2 | Viewed by 1558
Abstract
In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend [...] Read more.
In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
15 pages, 322 KiB  
Article
Fixed Points Theorems for Unsaturated and Saturated Classes of Contractive Mappings in Banach Spaces
by Vasile Berinde and Mădălina Păcurar
Symmetry 2021, 13(4), 713; https://doi.org/10.3390/sym13040713 - 18 Apr 2021
Cited by 14 | Viewed by 2194
Abstract
Based on the technique of enriching contractive type mappings, a technique that has been used successfully in some recent papers, we introduce the concept of a saturated class of contractive mappings. We show that, from this perspective, the contractive type mappings in the [...] Read more.
Based on the technique of enriching contractive type mappings, a technique that has been used successfully in some recent papers, we introduce the concept of a saturated class of contractive mappings. We show that, from this perspective, the contractive type mappings in the metric fixed point theory can be separated into two distinct classes, unsaturated and saturated, and that, for any unsaturated class of mappings, the technique of enriching contractive type mappings provides genuine new fixed-point results. We illustrate the concept by surveying some significant fixed-point results obtained recently for five remarkable unsaturated classes of contractive mappings. In the second part of the paper, we also identify two important classes of saturated contractive mappings, whose main feature is that they cannot be enlarged by enriching the contractive mappings. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
14 pages, 390 KiB  
Article
A Mean Extragradient Method for Solving Variational Inequalities
by Apichit Buakird, Nimit Nimana and Narin Petrot
Symmetry 2021, 13(3), 462; https://doi.org/10.3390/sym13030462 - 12 Mar 2021
Cited by 2 | Viewed by 1799
Abstract
We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull [...] Read more.
We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry)
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