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Advances in Fixed Point Theory and Its Applications
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Advances in Fixed Point Theory and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 21168

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Timilehin Opeyemi Alakoya

E-Mail Website
Guest Editor
School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK
Interests: nonlinear functional analysis; fixed point theory and applications; optimization problems; iterative methods

Special Issue Information

Dear Colleagues,

We invite you to contribute a manuscript to this Special Issue on “Advances in Fixed Point Theory and Its Applications”. Fixed point theory is a hot area of research. It has many applications in diverse fields ranging from different branches of mathematics to engineering, and from economics to biology. For example, optimization problems including minimization problems, variational inequality problems, equilibrium problems, and variational inclusion problems, among others, are known to be very useful in diverse fields such as economics, computer science, and engineering, and they find applications in machine learning. Many problems arising from these fields can be modeled as optimization problems. One of the most successful methods for solving optimization problems is the fixed-point method. As a result of this, recently, significant research efforts have been devoted to developing fixed point iterative methods for approximating solutions to optimization problems.

The aim of this Special Issue is to gather and publish new results on fixed point theory and its applications. We welcome papers on topics including, but not limited to the following:

  1. iterative methods;
  2. optimization and control;
  3. variational problems;
  4. numerical problems in dynamical systems;
  5. theory, methods, and applications of optimization;
  6. mathematical modeling via fixed point theory;
  7. applications of fixed point theory in engineering, science, and technology.

Dr. Timilehin Opeyemi Alakoya
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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
  • iterative methods
  • fixed-point iteration
  • variational problems
  • optimization and control
  • optimization theory, methods, and applications
  • applications of fixed point theory and approaches

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Published Papers (15 papers)

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Research

27 pages, 2341 KiB  
Article
An Algorithm That Adjusts the Stepsize to Be Self-Adaptive with an Inertial Term Aimed for Solving Split Variational Inclusion and Common Fixed Point Problems
by Matlhatsi Dorah Ngwepe, Lateef Olakunle Jolaoso, Maggie Aphane and Ibrahim Oyeyemi Adenekan
Mathematics 2023, 11(22), 4708; https://doi.org/10.3390/math11224708 - 20 Nov 2023
Cited by 1 | Viewed by 938
Abstract
In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every [...] Read more.
In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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19 pages, 326 KiB  
Article
Solving Integral Equation and Homotopy Result via Fixed Point Method
by Badriah Alamri
Mathematics 2023, 11(21), 4408; https://doi.org/10.3390/math11214408 - 24 Oct 2023
Cited by 1 | Viewed by 876
Abstract
The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (α,η,ψ)-contraction in the framework [...] Read more.
The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (α,η,ψ)-contraction in the framework of F-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in F-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
13 pages, 305 KiB  
Article
The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps
by Isaac Karabo Letlhage, Deepak Khantwal, Rajendra Pant and Manuel De la Sen
Mathematics 2023, 11(20), 4271; https://doi.org/10.3390/math11204271 - 13 Oct 2023
Viewed by 1026
Abstract
The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. [...] Read more.
The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for multi-valued maps and the concept of well-posedness. We present an application to a specific functional equation which arises in dynamic programming. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
14 pages, 289 KiB  
Article
Czerwik Vector-Valued Metric Space with an Equivalence Relation and Extended Forms of Perov Fixed-Point Theorem
by Monairah Alansari, Yahya Almalki and Muhammad Usman Ali
Mathematics 2023, 11(16), 3583; https://doi.org/10.3390/math11163583 - 18 Aug 2023
Cited by 1 | Viewed by 1075
Abstract
In this article, we shall generalize the idea of vector-valued metric space and Perov fixed-point theorem. We shall introduce the notion of Czerwik vector-valued R-metric space by involving an equivalence relation. A few basic concepts and properties related to Czerwik vector-valued R [...] Read more.
In this article, we shall generalize the idea of vector-valued metric space and Perov fixed-point theorem. We shall introduce the notion of Czerwik vector-valued R-metric space by involving an equivalence relation. A few basic concepts and properties related to Czerwik vector-valued R-metric space shall also be discussed that are required to obtain a few extended types of Perov fixed-point theorem. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
20 pages, 2628 KiB  
Article
A Novel Two-Step Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Image Recovery
by Rattanakorn Wattanataweekul, Kobkoon Janngam and Suthep Suantai
Mathematics 2023, 11(16), 3518; https://doi.org/10.3390/math11163518 - 15 Aug 2023
Cited by 4 | Viewed by 999
Abstract
This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The [...] Read more.
This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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22 pages, 323 KiB  
Article
Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method
by Yuan Meng, Conghong He, Renhao Ma and Huihui Pang
Mathematics 2023, 11(13), 2941; https://doi.org/10.3390/math11132941 - 30 Jun 2023
Viewed by 1010
Abstract
In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown functions and their fractional derivatives. Using the fixed point theorem for [...] Read more.
In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown functions and their fractional derivatives. Using the fixed point theorem for mixed monotone operators, we constructe iteration functions for arbitrary initial value and acquire the existence and uniqueness of extremal solutions. Moreover, a related example is given to illustrate our research results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
19 pages, 345 KiB  
Article
The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations
by Gunaseelan Mani, Salma Haque, Arul Joseph Gnanaprakasam, Ozgur Ege and Nabil Mlaiki
Mathematics 2023, 11(12), 2742; https://doi.org/10.3390/math11122742 - 16 Jun 2023
Cited by 4 | Viewed by 887
Abstract
In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing and expanding some recently established results. Finally, we explain an application of our main result to a certain type of [...] Read more.
In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing and expanding some recently established results. Finally, we explain an application of our main result to a certain type of fractional differential equation. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
14 pages, 331 KiB  
Article
(α − ψ) Meir–Keeler Contractions in Bipolar Metric Spaces
by Manoj Kumar, Pankaj Kumar, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, Amr Elsonbaty and Stojan Radenović
Mathematics 2023, 11(6), 1310; https://doi.org/10.3390/math11061310 - 8 Mar 2023
Cited by 2 | Viewed by 1323
Abstract
In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide [...] Read more.
In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide some corollaries of main results. An example is also be given in support of our main result. In the end, we also solve an integral equation using our result. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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9 pages, 268 KiB  
Article
New Versions of Some Results on Fixed Points in b-Metric Spaces
by Zoran D. Mitrović, Abasalt Bodaghi, Ahmad Aloqaily, Nabil Mlaiki and Reny George
Mathematics 2023, 11(5), 1118; https://doi.org/10.3390/math11051118 - 23 Feb 2023
Cited by 5 | Viewed by 1772
Abstract
The main and the most important objective of this paper is to nominate some new versions of several well-known results about fixed-point theorems such as Caristi’s theorem, Pant et al.’s theorem and Karapınar et al.’s theorem in the case of b-metric spaces. [...] Read more.
The main and the most important objective of this paper is to nominate some new versions of several well-known results about fixed-point theorems such as Caristi’s theorem, Pant et al.’s theorem and Karapınar et al.’s theorem in the case of b-metric spaces. We use a new technique provided by Miculescu and Mihail in order to prove our theorems. Some illustrative applications and examples are given to strengthen our new findings and the main results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
10 pages, 264 KiB  
Article
On Cyclic Contractive Mappings of Kannan and Chatterjea Type in Generalized Metric Spaces
by Mohammad Al-Khaleel, Sharifa Al-Sharif and Rami AlAhmad
Mathematics 2023, 11(4), 890; https://doi.org/10.3390/math11040890 - 9 Feb 2023
Cited by 5 | Viewed by 1580
Abstract
Novel cyclic contractions of the Kannan and Chatterjea type are presented in this study. With the aid of these brand-new contractions, new results for the existence and uniqueness of fixed points in the setting of complete generalized metric space have been established. Importantly, [...] Read more.
Novel cyclic contractions of the Kannan and Chatterjea type are presented in this study. With the aid of these brand-new contractions, new results for the existence and uniqueness of fixed points in the setting of complete generalized metric space have been established. Importantly, the results are generalizations and extensions of fixed point theorems by Chatterjea and Kannan and their cyclical expansions that are found in the literature. Additionally, several of the existing results on fixed points in generalized metric space will be generalized by the results presented in this work. Interestingly, the findings have a variety of applications in engineering and sciences. Examples have been given at the end to show the reliability of the demonstrated results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
18 pages, 437 KiB  
Article
New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications
by Arul Joseph Gnanaprakasam, Gunaseelan Mani, Ozgur Ege, Ahmad Aloqaily and Nabil Mlaiki
Mathematics 2023, 11(3), 677; https://doi.org/10.3390/math11030677 - 28 Jan 2023
Cited by 10 | Viewed by 2042
Abstract
In this article, we present the concept of orthogonal α-almost Istra˘tescu contraction of types D and D* and prove some fixed point theorems on orthogonal b-metric spaces. We also provide an illustrative example to support our theorems. [...] Read more.
In this article, we present the concept of orthogonal α-almost Istra˘tescu contraction of types D and D* and prove some fixed point theorems on orthogonal b-metric spaces. We also provide an illustrative example to support our theorems. As an application, we establish the existence and uniqueness of the solution of the fractional differential equation and the solution of the integral equation using Elzaki transform. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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26 pages, 591 KiB  
Article
A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets
by Timilehin Opeyemi Alakoya and Oluwatosin Temitope Mewomo
Mathematics 2023, 11(2), 386; https://doi.org/10.3390/math11020386 - 11 Jan 2023
Cited by 5 | Viewed by 1566
Abstract
Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple output sets. We propose a [...] Read more.
Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple output sets. We propose a new Tseng extragradient method, which uses self-adaptive step sizes for approximating the solution to the problem when the cost operators are pseudomonotone and non-Lipschitz in the framework of Hilbert spaces. We point out that while the cost operators are non-Lipschitz, our proposed method does not involve any linesearch procedure for its implementation. Instead, we employ a more efficient self-adaptive step size technique with known parameters. In addition, we employ the relaxation method and the inertial technique to improve the convergence properties of the algorithm. Moreover, under some mild conditions on the control parameters and without the knowledge of the operators’ norm, we prove that the sequence generated by our proposed method converges strongly to a minimum-norm solution to the problem. Finally, we apply our result to study certain classes of optimization problems, and we present several numerical experiments to demonstrate the applicability of our proposed method. Several of the existing results in the literature in this direction could be viewed as special cases of our results in this study. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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16 pages, 637 KiB  
Article
Study of Fractional Differential Equations Emerging in the Theory of Chemical Graphs: A Robust Approach
by Ali Turab and Norhayati Rosli
Mathematics 2022, 10(22), 4222; https://doi.org/10.3390/math10224222 - 11 Nov 2022
Cited by 7 | Viewed by 1477
Abstract
The study of the interconnections between chemical systems is known as chemical graph theory. Through the use of star graphs, a limited group of researchers has examined the space of possible solutions for boundary-value problems. They recognized that for their strategy to function, [...] Read more.
The study of the interconnections between chemical systems is known as chemical graph theory. Through the use of star graphs, a limited group of researchers has examined the space of possible solutions for boundary-value problems. They recognized that for their strategy to function, they needed a core node related to other nodes but not to itself; as a result, they opted to use star graphs. In this sense, the graphs of neopentane will be helpful in extending the scope of our technique. It has the CAS number 463-82-1 and the chemical formula C5H12, and it is a component of a petrochemical precursor. In order to determine whether or not the suggested boundary-value problems on these graphs have any known solutions, we use the theorems developed by Schaefer and Krasnoselskii on fixed points. In addition, we illustrate our preliminary results with the help of an example that we present. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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13 pages, 288 KiB  
Article
Generalized Contractions and Fixed Point Results in Spaces with Altering Metrics
by Adrian Nicolae Branga and Ion Marian Olaru
Mathematics 2022, 10(21), 4083; https://doi.org/10.3390/math10214083 - 2 Nov 2022
Cited by 3 | Viewed by 1292
Abstract
In this paper, we have provided some fixed point results for self-mappings fulfilling generalized contractive conditions on altered metric spaces. In addition, some applications of the main results to continuous data dependence of the fixed points of operators defined on these spaces were [...] Read more.
In this paper, we have provided some fixed point results for self-mappings fulfilling generalized contractive conditions on altered metric spaces. In addition, some applications of the main results to continuous data dependence of the fixed points of operators defined on these spaces were shown. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
26 pages, 427 KiB  
Article
Some New Results on Convergence, Weak w2-Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces
by Austine Efut Ofem, Jacob Ashiwere Abuchu, Reny George, Godwin Chidi Ugwunnadi and Ojen Kumar Narain
Mathematics 2022, 10(20), 3720; https://doi.org/10.3390/math10203720 - 11 Oct 2022
Cited by 14 | Viewed by 1437
Abstract
In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued mappings satisfying condition (E) in hyperbolic spaces. We consider new concepts of weak w2-stability [...] Read more.
In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued mappings satisfying condition (E) in hyperbolic spaces. We consider new concepts of weak w2-stability and data dependence results involving two multivalued almost contractive mappings. We provide examples of multivalued almost contractive mappings to show the advantage of our new iterative algorithm over some exiting iterative algorithms. Moreover, we prove several strong ∆-convergence theorems of our new algorithm in hyperbolic spaces. Furthermore, with another novel example, we carry out a numerical experiment to compare the efficiency and applicability of a new iterative algorithm with several leading iterative algorithms. The results in this article extend and improve several existing results from the setting of linear and CAT(0) spaces to hyperbolic spaces. Our main results also extend several existing results from the setting of single-valued mappings to the setting of multivalued mappings. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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