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Axioms
Special Issues
Fixed Point Theory and Its Applications
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Fixed Point Theory and Its Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 2232

Special Issue Editors

Prof. Dr. Lu-Chuan Ceng

E-Mail Website
Guest Editor
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Interests: nonlinear analysis; fixed point theory and applications; optimization problems; iterative methods
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jen-Chih Yao

E-Mail Website
Guest Editor
1. Research Center for Interneural Computing, China Medical University Hospital, Taichung City 404332, Taiwan
2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
Interests: vector optimization; fixed point theory; variational inequalities; complementarity problems; variational analysis; equilibrium problems; optimal control; generalized convexity and generalized monotonicity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

To the best of our understanding, the fixed point theory has been a hot research area. It has played a vital role in handling nonlinear phenomena of the real world. There have been numerous results regarding the existence, uniqueness and approximation of fixed points of nonlinear operators, and these also find numerous applications in pure and applied sciences. In particular, it has vast applications in various areas arising from optimization, engineering, economics and biology. Many optimization problems, such as minimization, variational inequalities, equilibria and variational inclusions, are known to be resolved by it and to be very helpful in various areas such as economics, computer science and engineering. In addition, they find applications in machine learning. Many problems originating in these areas can be modeled as optimization problems. At present, the fixed point method is one of the most effective approaches for solving optimization problems. Therefore, it is worth mentioning that meaningful research works have been focused on developing fixed point iterative methods for finding solutions to optimization problems.

This Special Issue aims to collect and publish novel and original 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.

Prof. Dr. Lu-Chuan Ceng
Prof. Dr. Jen-Chih 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. Axioms 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
  • iterative methods
  • bilevel optimization problems
  • optimization problems on Hadamard manifold
  • monotone inclusion problems
  • optimization and control
  • optimization theory, methods, and applications
  • applications of fixed point theory and approaches

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Published Papers (2 papers)

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Research

24 pages, 329 KiB  
Article
Exploring Fixed-Point Theorems in k-Fuzzy Metric Spaces: A Comprehensive Study
by Muhammad Nazam, Seemab Attique, Aftab Hussain and Hamed H. Alsulami
Axioms 2024, 13(8), 558; https://doi.org/10.3390/axioms13080558 - 15 Aug 2024
Viewed by 1038
Abstract
Recently, k -fuzzy metric spaces were introduced by connecting the degree of nearness of two points with k parameters (t1,t2,t3,⋯,tk) and the authors presented an analogue of Grabiec’s fixed-point [...] Read more.
Recently, k -fuzzy metric spaces were introduced by connecting the degree of nearness of two points with k parameters (t1,t2,t3,⋯,tk) and the authors presented an analogue of Grabiec’s fixed-point result in k-fuzzy metric spaces along with other necessary notions. The results presented only addressed continuous mappings. For discontinuous mappings, there is no result in k-fuzzy metric spaces. In this paper, we obtain some fixed-point results stating necessary conditions for the existence of fixed points of mappings eliminating the continuity requirement in k-fuzzy metric spaces. We illustrate the hypothesis of our findings with examples. We provide a common fixed-point theorem and fixed-point theorems for single-valued k-fuzzy Kannan type contractions. As an application, we use a fixed-point result to ensure the existence of solution of fractional differential equations. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications)
14 pages, 280 KiB  
Article
Fuzzy H-Quasi-Contraction and Fixed Point Theorems in Tripled Fuzzy Metric Spaces
by Yunpeng Zhao, Fei He and Xuan Liu
Axioms 2024, 13(8), 536; https://doi.org/10.3390/axioms13080536 - 7 Aug 2024
Viewed by 518
Abstract
We consider the concept of fuzzy H-quasi-contraction (FH-QC for short) initiated by Ćirić in tripled fuzzy metric spaces (T-FMSs for short) and present a new fixed point theorem ( [...] Read more.
We consider the concept of fuzzy H-quasi-contraction (FH-QC for short) initiated by Ćirić in tripled fuzzy metric spaces (T-FMSs for short) and present a new fixed point theorem (FPT for short) for FH-QC in complete T-FMSs. As an application, we prove the corresponding results of the previous literature in setting fuzzy metric spaces (FMSs for short). Moreover, we obtain theorems of sufficient and necessary conditions which can be used to demonstrate the existence of fixed points. In addition, we construct relevant examples to illustrate the corresponding results. Finally, we show the existence and uniqueness of solutions for integral equations by applying our new results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications)
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