Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.9
Journals
Axioms
Special Issues
Advances in Fixed Point Theory with Applications
share announcement

Advances in Fixed Point Theory with Applications

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 4795

Special Issue Editors

Prof. Dr. Sanda Micula

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Interests: numerical methods for integral equations and related problems; spline collocation; approximation theory
Special Issues, Collections and Topics in MDPI journals
Dr. Monica-Felicia Bota

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Interests: applied mathematics; metric spaces; nonlinear operators; fractal-fractional model; fractional derivative; FPDE; ODE; PDE
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fixed point theory is a captivating field with broad applications in various areas of mathematics. Notably, Brouwer’s fixed point theorem and Banach’s contraction principle are two of the most powerful and widely used theorems in this domain. Many researchers work on extending these classical theorems in new directions. The rapid developments in fixed point theory and its practical applications over recent decades have led to numerous and valuable academic papers underscoring its importance in nonlinear analysis, optimization problems, integral and differential equations, dynamical systems, control theory, numerical methods, signal and image processing, economics, and game theory, among many others. This Special Issue seeks to collect and publish new theoretical and numerical research studies in fixed point theory that effectively translate basic scientific concepts into real-world applications.

Many real-world problems can be addressed by solving mathematical models through computational analysis. In recent years, computational analysis has significantly enhanced our understanding of various fields, including immunological systems, computational systems, electrical and mechanical structures, financial markets, information and knowledge management, highway transportation networks, telecommunication networks, and economics. Given the importance of computational analysis, this Special Issue also invites contributions that describe the applications of mathematics and computation to these and other areas.

We cordially invite researchers to contribute their original and high-quality research papers to this Special Issue. Topics of interest include but are not limited to the following:

  • Fixed point theory and best proximity point theory with applications;
  • Fixed point theory for single-valued and multi-valued mappings in various abstract spaces with applications;
  • Fixed-point theorems satisfying distinctive contractive conditions and their applications;
  • Solvability of nonlinear differential and integral equations and inclusions;
  • Stability of functional equations and inclusions;
  • Fractional differential equations and inclusions;
  • Coincidence points and common fixed-points;
  • Unique and non-unique fixed-point theory;
  • Numerical algorithms for nonlinear problems;
  • Functional differential equations and inclusions;
  • Optimization problems by fixed point theory;
  • Geometry of Banach spaces;
  • Well-posedness and control in fixed point theory;
  • Successive approximations (such as Picard, Mann, Krasnoselskij, and Ishikawa iterations, and others);
  • Linear and nonlinear dynamical systems;
  • Applications to computer graphics.

We look forward to receiving your contributions.

Prof. Dr. Sanda Micula
Dr. Monica-Felicia Bota
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
  • well-posedness
  • stability
  • coincidence and common fixed points
  • abstract metric spaces
  • differential equations and inclusions
  • integral equations and inclusions
  • fractional differential equations and inclusions
  • iterative methods
  • dynamical systems

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

24 pages, 396 KiB  
Article
Four-Step T-Stable Generalized Iterative Technique with Improved Convergence and Various Applications
by Quanita Kiran and Shaista Begum
Axioms 2025, 14(1), 71; https://doi.org/10.3390/axioms14010071 - 20 Jan 2025
Viewed by 485
Abstract
This research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research also investigates convergence of the new iteration in uniformly convex [...] Read more.
This research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research also investigates convergence of the new iteration in uniformly convex Banach space and explores its stability. To further support our findings, we present its working on to a BV problem and to a delay DE. Finally, we propose a design of an implicit neural network that can be considered as an extension of a traditional feed forward network. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
►▼ Show Figures

Figure 1

19 pages, 266 KiB  
Article
Fixed-Point Results in Elliptic-Valued Metric Spaces with Applications
by Badriah Alamri
Axioms 2025, 14(1), 46; https://doi.org/10.3390/axioms14010046 - 8 Jan 2025
Viewed by 469
Abstract
The primary objective of this research is to investigate the notion of elliptic-valued metric spaces and prove new fixed-point theorems for diverse generalized contractions. Our contributions extend several existing results in the field. To underscore the novelty of our main result, we provide [...] Read more.
The primary objective of this research is to investigate the notion of elliptic-valued metric spaces and prove new fixed-point theorems for diverse generalized contractions. Our contributions extend several existing results in the field. To underscore the novelty of our main result, we provide a concrete example. Additionally, we showcase the practical relevance of our primary theorem by solving a Urysohn integral equation. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
21 pages, 343 KiB  
Article
Fixed-Point Results for Krasnoselskii, Meir–Keeler, and Boyd–Wong-Type Mappings with Applications to Dynamic Market Equilibrium
by Lifang Guo, Rabia Bibi, Abeer Alshejari, Ekrem Savas, Tayyab Kamran and Umar Ishtiaq
Axioms 2024, 13(12), 867; https://doi.org/10.3390/axioms13120867 (registering DOI) - 12 Dec 2024
Viewed by 649
Abstract
This paper introduces the idea of a cone m-hemi metric space, which extends the idea of an m-hemi metric space. By presenting non-trivial examples, we demonstrate the superiority of cone m-hemi metric spaces over m-hemi metric spaces. Further, we [...] Read more.
This paper introduces the idea of a cone m-hemi metric space, which extends the idea of an m-hemi metric space. By presenting non-trivial examples, we demonstrate the superiority of cone m-hemi metric spaces over m-hemi metric spaces. Further, we extend the Banach contraction principle and Krasnoselskii, Meir–Keeler, Boyd–Wong, and some other fixed-point results in the setting of complete and compact cone m-hemi metric spaces. Furthermore, we provide several non-trivial examples and applications to the Fredholm integral equation and dynamic market equilibrium to demonstrate the validity of the main results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
►▼ Show Figures

Figure 1

27 pages, 333 KiB  
Article
Fixed-Point Results for Multi-Valued Mappings in Topological Vector Space-Valued Cone Metric Spaces with Applications
by Hala Alzumi and Jamshaid Ahmad
Axioms 2024, 13(12), 841; https://doi.org/10.3390/axioms13120841 - 29 Nov 2024
Viewed by 492
Abstract
The objective of this research article is to introduce Kikkawa and Suzuki-type contractions in the setting of topological vector space-valued cone metric space with a solid cone and establish some new fixed point results for multi-valued mappings. The problem of finding fixed points [...] Read more.
The objective of this research article is to introduce Kikkawa and Suzuki-type contractions in the setting of topological vector space-valued cone metric space with a solid cone and establish some new fixed point results for multi-valued mappings. The problem of finding fixed points for multi-valued mappings satisfying locally contractive conditions on a closed ball is also addressed. Our findings generalize a number of well-established results in the literature. To highlight the uniqueness of our key finding, we present an example. As a demonstration of the applicability of our principal theorem, we prove a result in homotopy theory. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
16 pages, 287 KiB  
Article
An Averaged Halpern-Type Algorithm for Solving Fixed-Point Problems and Variational Inequality Problems
by Vasile Berinde and Khairul Saleh
Axioms 2024, 13(11), 756; https://doi.org/10.3390/axioms13110756 - 31 Oct 2024
Viewed by 559
Abstract
In this paper, we propose and study an averaged Halpern-type algorithm for approximating the solution of a common fixed-point problem for a couple of nonexpansive and demicontractive mappings with a variational inequality constraint in the setting of a Hilbert space. The strong convergence [...] Read more.
In this paper, we propose and study an averaged Halpern-type algorithm for approximating the solution of a common fixed-point problem for a couple of nonexpansive and demicontractive mappings with a variational inequality constraint in the setting of a Hilbert space. The strong convergence of the sequence generated by the algorithm is established under feasible assumptions on the parameters involved. In particular, we also obtain the common solution of the fixed point problem for nonexpansive or demicontractive mappings and of a variational inequality problem. Our results extend and generalize various important related results in the literature that were established for two pairs of mappings: (nonexpansive, nonspreading) and (nonexpansive, strongly quasi-nonexpansive). Numerical tests to illustrate the superiority of our algorithm over the ones existing in the literature are also reported. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
16 pages, 314 KiB  
Article
Fuzzy Fixed Point Theorems in S-Metric Spaces: Applications to Navigation and Control Systems
by Maryam Iqbal, Afshan Batool, Aftab Hussain and Hamed Alsulami
Axioms 2024, 13(9), 650; https://doi.org/10.3390/axioms13090650 - 22 Sep 2024
Viewed by 1521
Abstract
This manuscript examines fuzzy fixed point results using the concepts of S-metric space. We introduce two contractive maps, γ- and γ-weak contractions, within the context of S-metric spaces. These contractive maps form the cornerstone of our research, offering a [...] Read more.
This manuscript examines fuzzy fixed point results using the concepts of S-metric space. We introduce two contractive maps, γ- and γ-weak contractions, within the context of S-metric spaces. These contractive maps form the cornerstone of our research, offering a novel approach to solving mathematical problems. We explore fixed point results derived from the application of these maps, showcasing their utility in finding solutions in diverse mathematical scenarios. Furthermore, we provide concrete examples that illustrate the practical relevance and versatility of our theorems, emphasizing their potential applications across a wide range of scientific and engineering domains. This manuscript presents the novel concepts of γ- and γ-weak contractions and establishes their importance in mathematical research. By demonstrating their effectiveness in solving real-world problems and offering illustrative examples, our work contributes valuable tools and insights to the broader scientific community, enhancing our understanding of contractive maps and their applications. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop