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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 2025 | Viewed by 479

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 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

  • 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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Published Papers (2 papers)

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Research

24 pages, 3146 KiB  
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 177
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 KiB  
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
Viewed by 180
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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