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Mathematics
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Fixed Point Theory and Dynamical Systems with Applications
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Fixed Point Theory and Dynamical Systems with Applications

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

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 32946

Special Issue Editors

Prof. Dr. Wei-Shih Du

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Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Chung-Chuan Chen

E-Mail Website
Guest Editor
Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan
Interests: operator theory; functional analysis; abstract harmonic analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Marko Kostić

E-Mail Website
Guest Editor
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Interests: abstract Volterra integro-differential equations; abstract fractional differential equations; topological dynamics of linear operators and abstract PDEs
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Bessem Samet

E-Mail Website
Guest Editor
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Interests: fixed point
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since the celebrated Brouwer’s fixed point theorem and Banach contraction principle were established, the rapid growth of fixed point theory and its applications during the past more than a hundred years have led to a number of scholarly essays that study the importance of its promotion and application in nonlinear analysis, applied mathematical analysis, economics, game theory, integral and differential equations and inclusions, dynamic systems theory, signal and image processing, and so forth. Many authors devoted their attention to investigating generalizations in various different directions of the well-known fixed point theorems. Recent important investigations and developments in fixed point theory have been focused on putting fundamental sciences into the real world.

Dynamical systems, developed initially from the work of Jay W. Forrester, focused on industrial dynamics. During the previous more than six decades, important contributions to the improvement of our understanding of the real world around us have been made in various domains, such as economics, financial markets, environment, human behavior, strategic decision-making, information and knowledge management, public policy, highway transportation networks, telecommunication networks, immunological systems, computational systems, and electrical and mechanical structures. About three decades ago, linear dynamics and chaos started to attract a lot of attention, and fruitful results appeared. Nowadays, dynamical systems have already been developed and applied by policy-makers, academicians, educators, and managers in many areas of natural sciences, social sciences, engineering, and mathematical sciences.

We cordially and earnestly invite researchers to contribute their original and high-quality research papers which will inspire advances in fixed point theory, dynamical systems, and their applications. Potential topics include, but are not limited to:

  • Fixed point theory in various abstract spaces with applications
  • Best proximity point theory in various abstract spaces with applications
  • Algorithms for fixed points and best proximity points
  • Nonlinear differential and integral equations via fixed point theory approaches
  • Optimization problems via fixed point theory approaches
  • Well-posedness and control in fixed point theory and dynamical systems
  • Nonlinear and linear dynamical systems
  • Advanced control systems
  • Nonlinear waves and acoustics
  • Image and signal processing
  • Biological systems and bioinformatics

Prof. Dr. Wei-Shih Du
Prof. Dr. Chung-Chuan Chen
Prof. Dr. Marko Kostić
Prof. Dr. Bessem Samet
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

  • Fixed point theory
  • Best proximity point theory
  • Geometry of Banach spaces
  • Algorithm
  • Stability of functional equations
  • Nonlinear and linear dynamical systems
  • Control system
  • Image and signal processing
  • Biological systems and bioinformatics

Published Papers (15 papers)

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Editorial

Jump to: Research

2 pages, 179 KiB  
Editorial
Preface to the Special Issue “Fixed Point Theory and Dynamical Systems with Applications”
by Wei-Shih Du, Chung-Chuan Chen, Marko Kostić and Bessem Samet
Mathematics 2023, 11(13), 2813; https://doi.org/10.3390/math11132813 - 23 Jun 2023
Viewed by 658
Abstract
Since the celebrated Brouwer’s fixed point theorem and Banach contraction principle were established, the rapid growth of fixed point theory and its applications have led to a number of scholarly essays studying the importance of its promotion and application in nonlinear analysis, applied [...] Read more.
Since the celebrated Brouwer’s fixed point theorem and Banach contraction principle were established, the rapid growth of fixed point theory and its applications have led to a number of scholarly essays studying the importance of its promotion and application in nonlinear analysis, applied mathematical analysis, economics, game theory, integral and differential equations and inclusions, dynamic systems theory, signal and image processing, etc [...] Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)

Research

Jump to: Editorial

10 pages, 273 KiB  
Article
Fixed-Point Theorems in Fuzzy Metric Spaces via Fuzzy F-Contraction
by Huaping Huang, Biljana Carić, Tatjana Došenović, Dušan Rakić and Mirjana Brdar
Mathematics 2021, 9(6), 641; https://doi.org/10.3390/math9060641 - 17 Mar 2021
Cited by 14 | Viewed by 1899
Abstract
The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that [...] Read more.
The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F-contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
11 pages, 269 KiB  
Article
On Jungck–Branciari–Wardowski Type Fixed Point Results
by Biljana Carić, Tatjana Došenović, Reny George, Zoran D. Mitrović and Stojan Radenović
Mathematics 2021, 9(2), 161; https://doi.org/10.3390/math9020161 - 14 Jan 2021
Cited by 8 | Viewed by 1632
Abstract
The terms of F−integral contraction as well as (ϖ,ζ˜,F,i)−integral contraction are introduced. Fixed point and common fixed point theorems are established. For the mapping F we use only the supposition [...] Read more.
The terms of F−integral contraction as well as (ϖ,ζ˜,F,i)−integral contraction are introduced. Fixed point and common fixed point theorems are established. For the mapping F we use only the supposition that it is strictly increasing. As a consequence of the main theorems we obtain Jungck–Wardowski, Branciari–Wardowski and Jungck–Branciari type results. Consequently, the results presented in the article enhance and complement some known results in literature. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
21 pages, 295 KiB  
Article
A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces
by Yuanheng Wang, Cancan Li and Lirong Lu
Mathematics 2020, 8(11), 1944; https://doi.org/10.3390/math8111944 - 04 Nov 2020
Cited by 4 | Viewed by 1244
Abstract
We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence [...] Read more.
We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence generated by our new viscosity iterative scheme to approximate their common solutions are proved. As an application of our main results, we solve the standard constrained convex optimization problem. The results here generalize and improve some other authors’ recently corresponding results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
26 pages, 415 KiB  
Article
Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents, Part II
by Marko Kostić and Wei-Shih Du
Mathematics 2020, 8(7), 1052; https://doi.org/10.3390/math8071052 - 30 Jun 2020
Cited by 11 | Viewed by 1523
Abstract
In this paper, we introduce and analyze several different notions of almost periodic type functions and uniformly recurrent type functions in Lebesgue spaces with variable exponent L p ( x ) . We primarily consider the Stepanov and Weyl classes of generalized almost [...] Read more.
In this paper, we introduce and analyze several different notions of almost periodic type functions and uniformly recurrent type functions in Lebesgue spaces with variable exponent L p ( x ) . We primarily consider the Stepanov and Weyl classes of generalized almost periodic type functions and generalized uniformly recurrent type functions. We also investigate the invariance of generalized almost periodicity and generalized uniform recurrence with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract fractional differential inclusions in Banach spaces. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
21 pages, 850 KiB  
Article
Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents
by Marko Kostić and Wei-Shih Du
Mathematics 2020, 8(6), 928; https://doi.org/10.3390/math8060928 - 05 Jun 2020
Cited by 11 | Viewed by 1729
Abstract
In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the [...] Read more.
In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
10 pages, 237 KiB  
Article
On Wong Type Contractions
by Erdal Karapınar and Andreea Fulga
Mathematics 2020, 8(4), 649; https://doi.org/10.3390/math8040649 - 23 Apr 2020
Cited by 2 | Viewed by 1907
Abstract
In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results [...] Read more.
In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
18 pages, 325 KiB  
Article
The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions
by Nawab Hussain, Ghada Ali, Iram Iqbal and Bessem Samet
Mathematics 2020, 8(2), 212; https://doi.org/10.3390/math8020212 - 07 Feb 2020
Cited by 10 | Viewed by 1945
Abstract
In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which [...] Read more.
In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
12 pages, 748 KiB  
Article
Second-Order Parametric Free Dualities for Complex Minimax Fractional Programming
by Tone-Yau Huang
Mathematics 2020, 8(1), 67; https://doi.org/10.3390/math8010067 - 02 Jan 2020
Cited by 5 | Viewed by 1467
Abstract
In this paper, we will consider a minimax fractional programming in complex spaces. Since a duality model in a programming problem plays an important role, we will establish the second-order Mond–Weir type and Wolfe type dual models, and derive the weak, strong, and [...] Read more.
In this paper, we will consider a minimax fractional programming in complex spaces. Since a duality model in a programming problem plays an important role, we will establish the second-order Mond–Weir type and Wolfe type dual models, and derive the weak, strong, and strictly converse duality theorems. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
14 pages, 273 KiB  
Article
Topological Properties of E-Metric Spaces with Applications to Fixed Point Theory
by Huaping Huang
Mathematics 2019, 7(12), 1222; https://doi.org/10.3390/math7121222 - 11 Dec 2019
Cited by 10 | Viewed by 2677
Abstract
The purpose of this paper is to present some topological properties in E-metric spaces such as the properties of e-sequences, the decision conditions of e-Cauchy sequences, the characteristics of non-normal cones, and so on. Moreover, the theorem of nested closed-balls [...] Read more.
The purpose of this paper is to present some topological properties in E-metric spaces such as the properties of e-sequences, the decision conditions of e-Cauchy sequences, the characteristics of non-normal cones, and so on. Moreover, the theorem of nested closed-balls in such spaces is displayed. In addition, some principal applications to fixed point theory are also given. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
10 pages, 743 KiB  
Article
A New Fixed Point Result of Perov Type and Its Application to a Semilinear Operator System
by Ishak Altun, Nawab Hussain, Muhammad Qasim and Hamed H. Al-Sulami
Mathematics 2019, 7(11), 1019; https://doi.org/10.3390/math7111019 - 28 Oct 2019
Cited by 12 | Viewed by 1836
Abstract
In this paper, we present a new generalization of the Perov fixed point theorem on vector-valued metric space. Moreover, to show the significance of our result, we present both a nontrivial comparative example and an application to a kind of semilinear operator system [...] Read more.
In this paper, we present a new generalization of the Perov fixed point theorem on vector-valued metric space. Moreover, to show the significance of our result, we present both a nontrivial comparative example and an application to a kind of semilinear operator system about the existence of its solution. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
11 pages, 293 KiB  
Article
Some New Observations on Geraghty and Ćirić Type Results in b-Metric Spaces
by Nabil Mlaiki, Neboǰša Dedovic, Hassen Aydi, Milanka Gardašević-Filipović, Bandar Bin-Mohsin and Stojan Radenović
Mathematics 2019, 7(7), 643; https://doi.org/10.3390/math7070643 - 18 Jul 2019
Cited by 19 | Viewed by 2529
Abstract
We discuss recent fixed point results in b-metric spaces given by Pant and Panicker (2016). Our results are with shorter proofs. In addition, for ε ∈ ( 1 , 3 ] , our results are genuine generalizations of ones from Pant and [...] Read more.
We discuss recent fixed point results in b-metric spaces given by Pant and Panicker (2016). Our results are with shorter proofs. In addition, for ε ∈ ( 1 , 3 ] , our results are genuine generalizations of ones from Pant and Panicker. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
17 pages, 308 KiB  
Article
On Some New Fixed Point Results in Complete Extended b-Metric Spaces
by Quanita Kiran, Nayab Alamgir, Nabil Mlaiki and Hassen Aydi
Mathematics 2019, 7(5), 476; https://doi.org/10.3390/math7050476 - 25 May 2019
Cited by 15 | Viewed by 3674
Abstract
In this paper, we specified a method that generalizes a number of fixed point results for single and multi-valued mappings in the structure of extended b-metric spaces. Our results extend several existing ones including the results of Aleksic et al. for single-valued [...] Read more.
In this paper, we specified a method that generalizes a number of fixed point results for single and multi-valued mappings in the structure of extended b-metric spaces. Our results extend several existing ones including the results of Aleksic et al. for single-valued mappings and the results of Nadler and Miculescu et al. for multi-valued mappings. Moreover, an example is given at the end to show the superiority of our results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
14 pages, 264 KiB  
Article
Generalized (ψ,α,β)—Weak Contractions for Initial Value Problems
by Piyachat Borisut, Poom Kumam, Vishal Gupta and Naveen Mani
Mathematics 2019, 7(3), 266; https://doi.org/10.3390/math7030266 - 15 Mar 2019
Cited by 20 | Viewed by 2888
Abstract
A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation [...] Read more.
A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
8 pages, 2869 KiB  
Article
A New Family of Chaotic Systems with Different Closed Curve Equilibrium
by Xinhe Zhu and Wei-Shih Du
Mathematics 2019, 7(1), 94; https://doi.org/10.3390/math7010094 - 17 Jan 2019
Cited by 14 | Viewed by 2983
Abstract
Chaotic systems with hidden attractors, infinite number of equilibrium points and different closed curve equilibrium have received much attention in the past six years. In this work, we introduce a new family of chaotic systems with different closed curve equilibrium. Using the methods [...] Read more.
Chaotic systems with hidden attractors, infinite number of equilibrium points and different closed curve equilibrium have received much attention in the past six years. In this work, we introduce a new family of chaotic systems with different closed curve equilibrium. Using the methods of equilibrium points, phase portraits, maximal Lyapunov exponents, Kaplan–Yorke dimension, and eigenvalues, we analyze the dynamical properties of the proposed systems and extend the general knowledge of such systems. Full article
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
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