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Mathematics
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Fixed Point, Optimization, and Applications: 3rd Edition
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Fixed Point, Optimization, and Applications: 3rd Edition

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 6000

Special Issue Editors

Prof. Dr. Mihai Postolache

grade E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University Politehnica of Bucharest, Bucharest, Romania
Interests: fixed point theory; continuous optimization; numerical algorithms
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yonghong Yao

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Interests: nonlinear analysis; optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is well known that fixed point theory in suitable spaces is an active research area nowadays. This is due to its versatility in studying nonlinear phenomena of the real world. Results regarding the existence, uniqueness, and numerical reckoning of fixed points of nonlinear operators find diverse applications in theoretical and applied sciences.

Optimization is important in studying characteristics that describe diverse nonlinear phenomena of the real world, such as efficiency, control, and much more. The research topics in this field include best approximation, numerical algorithms, optimal control, and well-posedness.

This Special Issue aims to report new results in the two research areas recorded above: fixed point and optimization and their applications. This Special Issue will accept high-quality papers containing original research results with illustrative applications and survey articles of exceptional merit.

The research topics include, but are not limited to, the following:

  • The existence and uniqueness of fixed points;
  • Best approximation problems;
  • Iteration processes for fixed points or best proximity points;
  • Nonlinear optimization and applications;
  • Variational inequalities and equilibrium problems;
  • Dynamical systems and special functions;
  • Well-posedness and optimal control.

Prof. Dr. Mihai Postolache
Prof. Dr. Yonghong Yao
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 250 words) can be sent to the Editorial Office for assessment.

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

  • the existence and uniqueness of fixed points
  • best approximation problems
  • iteration processes for fixed points or best proximity points
  • nonlinear optimization and applications
  • variational inequalities and equilibrium problems
  • dynamical systems and special functions
  • well-posedness and optimal control

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Related Special Issues

Published Papers (8 papers)

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Research

14 pages, 314 KB  
Article
A Class of Relational Almost Nonlinear Contractions Using (c)-Comparison Functions with an Application in Nonlinear Integral Equations
by Doaa Filali, Esmail Alshaban, Ahmed Alamer, Bassam Z. Albalawi, Adel Alatawi and Faizan Ahmad Khan
Mathematics 2026, 14(5), 905; https://doi.org/10.3390/math14050905 - 6 Mar 2026
Viewed by 290
Abstract
This work uses (c)-comparison functions in a metric space endowed with an arbitrary binary relation to establish certain fixed point results under a nonlinear version of almost contractions. The findings addressed here generalize and extend a number of recent findings. A few scenarios [...] Read more.
This work uses (c)-comparison functions in a metric space endowed with an arbitrary binary relation to establish certain fixed point results under a nonlinear version of almost contractions. The findings addressed here generalize and extend a number of recent findings. A few scenarios are described to demonstrate the validity of our results. The legitimacy of the unique solution of a nonlinear integral problem is assessed utilizing our findings. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
18 pages, 912 KB  
Article
Some Modified Mann-Type Inertial Forward–Backward Iterative Methods for Monotone Inclusion Problems
by Mohammad Dilshad, Ibrahim Al-Dayel, Esmail Alshaban and Md. Nasiruzzaman
Mathematics 2025, 13(24), 4000; https://doi.org/10.3390/math13244000 - 15 Dec 2025
Viewed by 405
Abstract
In this paper, we propose three variants of Mann-type inertial forward–backward iterative methods for approximating the minimum-norm solution of the monotone inclusion problem and the fixed points of nonexpansive mappings. In the first two methods, we compute the Mann-type iteration together with the [...] Read more.
In this paper, we propose three variants of Mann-type inertial forward–backward iterative methods for approximating the minimum-norm solution of the monotone inclusion problem and the fixed points of nonexpansive mappings. In the first two methods, we compute the Mann-type iteration together with the inertial extrapolation and fixed-point iteration in the initiation of the process, while the last method computes only the Mann-type iteration with inertial extrapolation at the start of the process. We establish the strong convergence results for each method with appropriate assumptions and discuss some applications of the presented methods. Finally, we present numerical examples in both finite- and infinite-dimensional Hilbert spaces to demonstrate their efficiency. A comparative analysis with existing methods is also provided. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
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21 pages, 304 KB  
Article
Some Common Best Proximity Point Results in Neutrosophic Complete Metric Spaces
by Qiming Zhao, A. Sreelakshmi Unni, V. Pragadeeswarar and Yongqiao Wang
Mathematics 2025, 13(23), 3819; https://doi.org/10.3390/math13233819 - 28 Nov 2025
Viewed by 388
Abstract
In this research article, we prove the existence and uniqueness of common best proximity points for a given class of discontinuous mappings. For that, we have introduced the notions of neutrosophic proximally compatible mappings, neutrosophic proximally reciprocal and weak reciprocal mappings, and R [...] Read more.
In this research article, we prove the existence and uniqueness of common best proximity points for a given class of discontinuous mappings. For that, we have introduced the notions of neutrosophic proximally compatible mappings, neutrosophic proximally reciprocal and weak reciprocal mappings, and R-proximally weak reciprocal commuting mappings of type I and type II. We have given examples to validate our findings. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
21 pages, 352 KB  
Article
On α-ψ-Contractive Condition for Single-Valued and Multi-Valued Operators in Strong b-Metric Spaces
by Saud M. Alsulami and Thanaa A. Alarfaj
Mathematics 2025, 13(20), 3357; https://doi.org/10.3390/math13203357 - 21 Oct 2025
Cited by 1 | Viewed by 663
Abstract
This paper aims to establish fixed point theorems in a complete strong b-metric space under the α-ψ-contractive condition imposed on single-valued mappings. Subsequently, we prove certain fixed point theorems, both locally and globally, under the α∗-ψ [...] Read more.
This paper aims to establish fixed point theorems in a complete strong b-metric space under the α-ψ-contractive condition imposed on single-valued mappings. Subsequently, we prove certain fixed point theorems, both locally and globally, under the α∗-ψ-contractive condition and the α-ψ-contractive condition on multi-valued mappings in a complete strong b-metric space. The theorems presented in this paper extend, generalize, and improve various existing results in the literature. To demonstrate the superiority of the results, we present multiple examples throughout this article and two applications: one in dynamic programming and another in ordinary differential equations. Moreover, the proposed results provide stronger and more general conclusions compared to several well-known fixed point theorems in the literature. In particular, our findings highlight the novelty and superiority of the α-ψ-contractive framework in the setting of strong b-metric spaces, offering broader applicability and deeper insight into both theoretical and applied contexts. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
11 pages, 452 KB  
Article
A Banach Space Leap: Contraction Mapping Solutions for Stochastic Delay Systems
by Fatin Nabila Abd Latiff, Dawn A. Stoner, Kah Lun Wang and Kok Bin Wong
Mathematics 2025, 13(18), 3002; https://doi.org/10.3390/math13183002 - 17 Sep 2025
Viewed by 877
Abstract
We investigate the solvability and stability properties of a class of nonlinear stochastic delay differential equations (SDDEs) driven by Wiener noise and incorporating discrete time delays. The equations are formulated within a Banach space of continuous, adapted sample paths. Under standard Lipschitz and [...] Read more.
We investigate the solvability and stability properties of a class of nonlinear stochastic delay differential equations (SDDEs) driven by Wiener noise and incorporating discrete time delays. The equations are formulated within a Banach space of continuous, adapted sample paths. Under standard Lipschitz and linear growth conditions, we construct a solution operator and prove the existence and uniqueness of strong solutions using a fixed-point argument. Furthermore, we derive exponential mean-square stability via Lyapunov-type techniques and delay-dependent inequalities. This framework provides a unified and flexible approach to SDDE analysis that departs from traditional Hilbert space or semigroup-based methods. We explore a Banach space fixed-point approach to SDDEs with multiplicative noise and discrete delays, providing a novel functional-analytic framework for examining solvability and stability. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
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14 pages, 2664 KB  
Article
On Sn Iteration for Fixed Points of (E)-Operators with Numerical Analysis and Polynomiography
by Cristian Ciobanescu
Mathematics 2025, 13(16), 2625; https://doi.org/10.3390/math13162625 - 15 Aug 2025
Cited by 1 | Viewed by 900
Abstract
The first part of this study is related to the search of fixed points for (E)-operators (Garcia-Falset operators), in the Banach setting, by means of a three-step iteration procedure. The main results reveal some conclusions related to weak and strong convergence [...] Read more.
The first part of this study is related to the search of fixed points for (E)-operators (Garcia-Falset operators), in the Banach setting, by means of a three-step iteration procedure. The main results reveal some conclusions related to weak and strong convergence of the considered iterative scheme toward a fixed point. On the other hand, the usefulness of the Sn iterative scheme is once again revealed by demonstrating through numerical simulations the advantages of using it for solving the problem of the maximum modulus of complex polynomials compared to standard algorithms, such as Newton, Halley, or Kalantary’s so-called B4 iteration. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
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24 pages, 3146 KB  
Article
Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
by Kanyuta Poochinapan, Sompop Moonchai, Tanadon Chaobankoh and Phakdi Charoensawan
Mathematics 2025, 13(10), 1569; https://doi.org/10.3390/math13101569 - 9 May 2025
Viewed by 1105
Abstract
A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular [...] Read more.
A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order boundary value problems. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
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42 pages, 4959 KB  
Article
Fixed Points of Self-Mappings with Jumping Effects: Application to Stability of a Class of Impulsive Dynamic Systems
by Manuel De la Sen, Asier Ibeas, Aitor J. Garrido and Izaskun Garrido
Mathematics 2025, 13(7), 1157; https://doi.org/10.3390/math13071157 - 31 Mar 2025
Cited by 2 | Viewed by 611
Abstract
This paper studies the boundedness and convergence properties of the sequences generated by strict and weak contractions in metric spaces, as well as their fixed points, in the event that finite jumps can take place from the left to the right limits of [...] Read more.
This paper studies the boundedness and convergence properties of the sequences generated by strict and weak contractions in metric spaces, as well as their fixed points, in the event that finite jumps can take place from the left to the right limits of the successive values of the generated sequences. An application is devoted to the stabilization and the asymptotic stabilization of impulsive linear time-varying dynamic systems of the n-th order. The impulses are formalized based on the theory of Dirac distributions. Several results are stated and proved, namely, (a) for the case when the time derivative of the differential system is impulsive at isolated time instants; (b) for the case when the matrix function of dynamics is almost everywhere differentiable with impulsive effects at isolated time instants; and (c) for the case of combinations of the two above effects, which can either jointly take place at the same time instants or at distinct time instants. In the first case, finite discontinuities of the first order in the solution are generated; that is, equivalently, finite jumps take place between the corresponding left and right limits of the solution at the impulsive time instants. The second case generates, equivalently, finite jumps in the first derivative of the solution with respect to time from their left to their right limits at the corresponding impulsive time instants. Finally, the third case exhibits both of the above effects in a combined way. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
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