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Special Issue in Honor of the 60th Birthday of Professor...
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Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 36112

Printed Edition Available!
A printed edition of this Special Issue is available here.

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; fixed point theory and its applications; variational principles and inequalities; optimization theory; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luigi Muglia

E-Mail Website
Guest Editor
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende CS, Italy
Interests: ordinary differential equations; impulsive equations; iterative methods for fixed points
Prof. Dr. Adrian Petruşel

E-Mail Website
Guest Editor
1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University Cluj-Napoca, Mihail Kogălniceanu Street, no. 1, 400084 Cluj-Napoca, Romania
2. Academy of Romanian Scientists, Splaiul Independenţei Street, no. 54, Sector 5, RO-050094 Bucharest, Romania
Interests: fixed point theory; differential equations and integral equations; differential and integral inclusions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Professor Hong-Kun Xu received his PhD degree from Xi’an Jiaotong University in 1988 and is currently a distinguished professor at Hangzhou Dianzi University, China. In 2004, he received the South African Mathematical Society Research Distinction Award and a Second Prize of Natural Science of the Ministry of Education of China. He is the Former Head of the Department of Applied Mathematics and Dean of the College of Science at National Sun Yat-sen University, Taiwan. He was elected as a member of the Academy of Science of South Africa in 2005, and a fellow to the Academy of Sciences for the Developing World (TWAS) in 2012, selected at the “Thousand Talents Program” of Zhejiang Province in 2014, selected as a Thomson Reuters/Clarivate Highly Cited Researcher from 2014 to 2018, and a 2019 Elsevier Chinese Highly Cited Researcher. He has published approximately 250 research papers in journals and has delivered academic speeches (invited/keynote/plenary) at more than 50 international academic conferences. He is serving editorial boards for more than 20 international mathematical journals, including co-editor-in-chief of the Springer relaunched journal of Fixed Point Theory and Algorithms for Sciences and Engineering, and field editor-in-chief for the Fixed Point Theory and Optimization Sections of Frontiers in Applied Mathematics and Statistics. His main research interests include nonlinear functional analysis, optimization theory and algorithms, Banach space geometry theory, fixed point theory and applications, nonlinear mapping iteration method, inverse problem and its regularization method, financial mathematics, and so forth.

The purpose of this Special Issue is to pay tribute to the significant contributions in these fields of Professor Hong-Kun Xu and provide some important recent advances in theory, methods, and applications. We cordially and earnestly invite researchers to contribute their original and high-quality research papers which will inspire advances in nonlinear analysis, optimization, and their applications. Potential topics include, but are not limited to:

  • Fixed point, coincidence point, and best proximity point theory with applications
  • Algorithms for nonlinear problems
  • Set-valued analysis
  • Nonlinear and variational methods for ODEs and PDEs
  • Non-smooth analysis and optimization
  • Convex analysis
  • Matrix theory
  • Control theory
  • Inverse and ill-posed problems
  • Game theory
  • Dynamical systems
  • Image and signal processing
  • Data mining
Prof. Dr. Wei-Shih Du

Prof. Dr. Luigi Muglia
Prof. Dr. Adrian Petruşel
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, coincidence point and best proximity point theory
  • Algorithms
  • Set-valued analysis
  • Optimization
  • ODEs and PDEs
  • Non-smooth analysis
  • Variational analysis
  • Game theory
  • Convex analysis
  • Matrix theory
  • Control theory
  • Dynamical systems
  • Image and signal processing
  • Data mining

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Published Papers (17 papers)

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Editorial

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3 pages, 392 KiB  
Editorial
Editorial Conclusion for the Special Issue “Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu”
by Wei-Shih Du, Luigi Muglia and Adrian Petruşel
Axioms 2023, 12(6), 548; https://doi.org/10.3390/axioms12060548 - 1 Jun 2023
Viewed by 1131
Abstract
In the original article [...] Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)

Research

Jump to: Editorial

10 pages, 264 KiB  
Article
The Asymptotic Behavior for Generalized Jiřina Process
by You Lv and Huaping Huang
Axioms 2023, 12(1), 13; https://doi.org/10.3390/axioms12010013 - 23 Dec 2022
Cited by 1 | Viewed by 1178
Abstract
As the classic branching process, the Galton-Watson process has obtained intensive attentions in the past decades. However, this model has two idealized assumptions–discrete states and time-homogeneity. In the present paper, we consider a branching process with continuous states, and for any given [...] Read more.
As the classic branching process, the Galton-Watson process has obtained intensive attentions in the past decades. However, this model has two idealized assumptions–discrete states and time-homogeneity. In the present paper, we consider a branching process with continuous states, and for any given n∈N, the branching law of every particle in generation n is determined by the population size of generation n. We consider the case that the process is extinct with Probability 1 since in this case the process will be substantially different from the size-dependent branching process with discrete states. We give the extinction rate in the sense of L2 and almost surely by the form of harmonic moments, that is to say, we show how fast {Zn−1} grows under a group of sufficient conditions. From the result of the present paper, we observe that the extinction rate will be determined by an asymptotic behavior of the mean of the branching law. The results obtained in this paper have the more superiority than the counterpart from the existing literature. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
10 pages, 267 KiB  
Article
Second-Ordered Parametric Duality for the Multi-Objective Programming Problem in Complex Space
by Chia-Yu Hsu and Tone-Yau Huang
Axioms 2022, 11(12), 717; https://doi.org/10.3390/axioms11120717 - 11 Dec 2022
Cited by 2 | Viewed by 1079
Abstract
We introduced and discussed a second-ordered parametric dual model of a complex multi-objective programming problem (P). Moreover, the authors constructed and proved the weak, strong and strictly converse duality theorems by the second-ordered generalized Θ-bonvexity. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
16 pages, 317 KiB  
Article
Optimality Conditions and Dualities for Robust Efficient Solutions of Uncertain Set-Valued Optimization with Set-Order Relations
by Yuwen Zhai, Qilin Wang and Tian Tang
Axioms 2022, 11(11), 648; https://doi.org/10.3390/axioms11110648 - 16 Nov 2022
Cited by 3 | Viewed by 1831
Abstract
In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on. By the new subdifferential and its properties, we establish a necessary and sufficient optimality condition of set-based robust efficient [...] Read more.
In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on. By the new subdifferential and its properties, we establish a necessary and sufficient optimality condition of set-based robust efficient solutions for the uncertain set-valued optimization problem. We also introduce a Wolfe type dual problem of the uncertain set-valued optimization problem. Finally, we establish the robust weak duality theorem and the robust strong duality theorem between the uncertain set-valued optimization problem and its robust dual problem. Several main results extend to the corresponding ones in the literature. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
14 pages, 285 KiB  
Article
Boundedness of Riesz Potential Operator on Grand Herz-Morrey Spaces
by Babar Sultan, Fatima Azmi, Mehvish Sultan, Mazhar Mehmood and Nabil Mlaiki
Axioms 2022, 11(11), 583; https://doi.org/10.3390/axioms11110583 - 24 Oct 2022
Cited by 17 | Viewed by 1638
Abstract
In this paper, we introduce grand Herz–Morrey spaces with variable exponent and prove the boundedness of Riesz potential operators in these spaces. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
9 pages, 258 KiB  
Article
Fixed Point Theory for Multi-Valued Feng–Liu–Subrahmanyan Contractions
by Claudia Luminiţa Mihiţ, Ghiocel Moţ and Adrian Petruşel
Axioms 2022, 11(10), 563; https://doi.org/10.3390/axioms11100563 - 17 Oct 2022
Cited by 4 | Viewed by 1549
Abstract
In this paper, we consider several problems related to the so-called multi-valued Feng–Liu–Subrahmanyan contractions in complete metric spaces. Existence of the fixed points and of the strict fixed points, as well as data dependence and stability properties for the fixed point problem, are [...] Read more.
In this paper, we consider several problems related to the so-called multi-valued Feng–Liu–Subrahmanyan contractions in complete metric spaces. Existence of the fixed points and of the strict fixed points, as well as data dependence and stability properties for the fixed point problem, are discussed. Some results are presented, under appropriate conditions, and some open questions are pointed out. Our results extend recent results given for multi-valued graph contractions and multi-valued Subrahmanyan contractions. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
23 pages, 524 KiB  
Article
Plane Section Curves on Surfaces of NCP Functions
by Shun-Wei Li, Yu-Lin Chang and Jein-Shan Chen
Axioms 2022, 11(10), 557; https://doi.org/10.3390/axioms11100557 - 14 Oct 2022
Cited by 1 | Viewed by 1469
Abstract
The goal of this paper is to investigate the curves intersected by a vertical plane with the surfaces based on certain NCP functions. The convexity and differentiability of these curves are studied as well. In most cases, the inflection points of the curves [...] Read more.
The goal of this paper is to investigate the curves intersected by a vertical plane with the surfaces based on certain NCP functions. The convexity and differentiability of these curves are studied as well. In most cases, the inflection points of the curves cannot be expressed exactly. Therefore, we instead estimate the interval where the curves are convex under this situation. Then, with the help of differentiability and convexity, we obtain the local minimum or maximum of the curves accordingly. The study of these curves is very useful to binary quadratic programming. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
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9 pages, 252 KiB  
Article
On a New Integral Inequality: Generalizations and Applications
by Huaping Huang and Wei-Shih Du
Axioms 2022, 11(9), 458; https://doi.org/10.3390/axioms11090458 - 6 Sep 2022
Cited by 1 | Viewed by 1581
Abstract
In this paper, we present some generalizations and improvements of a new integral inequality from the 29th IMC in 2022. Some applications of our new results are also provided. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
11 pages, 273 KiB  
Article
Some Common Fixed-Circle Results on Metric Spaces
by Nabil Mlaiki, Nihal Taş, Elif Kaplan, Suhad Subhi Aiadi and Asma Karoui Souayah
Axioms 2022, 11(9), 454; https://doi.org/10.3390/axioms11090454 - 4 Sep 2022
Cited by 5 | Viewed by 1476
Abstract
Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to an open problem CC: what is (are) the condition(s) to make any circle [...] Read more.
Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to an open problem CC: what is (are) the condition(s) to make any circle Cϖ0,σ as the common fixed circle for two (or more than two) self-mappings? To do this, we modify some known contractions which are used in fixed-point theorems such as the Hardy–Rogers-type contraction, Kannan-type contraction, etc. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
25 pages, 1505 KiB  
Article
A Non-Standard Finite Difference Scheme for a Diffusive HIV-1 Infection Model with Immune Response and Intracellular Delay
by Xiao-Lan Liu and Cheng-Cheng Zhu
Axioms 2022, 11(3), 129; https://doi.org/10.3390/axioms11030129 - 12 Mar 2022
Cited by 7 | Viewed by 2265
Abstract
In this paper, we propose and study a diffusive HIV infection model with infected cells delay, virus mature delay, abstract function incidence rate and a virus diffusion term. By introducing the reproductive numbers for viral infection R0 and for CTL immune response [...] Read more.
In this paper, we propose and study a diffusive HIV infection model with infected cells delay, virus mature delay, abstract function incidence rate and a virus diffusion term. By introducing the reproductive numbers for viral infection R0 and for CTL immune response number R1, we show that R0 and R1 act as threshold parameter for the existence and stability of equilibria. If R0≤1, the infection-free equilibrium E0 is globally asymptotically stable, and the viruses are cleared; if R1≤1<R0, the CTL-inactivated equilibrium E1 is globally asymptotically stable, and the infection becomes chronic but without persistent CTL response; if R1>1, the CTL-activated equilibrium E2 is globally asymptotically stable, and the infection is chronic with persistent CTL response. Next, we study the dynamic of the discreted system of our model by using non-standard finite difference scheme. We find that the global stability of the equilibria of the continuous model and the discrete model is not always consistent. That is, if R0≤1, or R1≤1<R0, the global stability of the two kinds model is consistent. However, if R1>1, the global stability of the two kinds model is not consistent. Finally, numerical simulations are carried out to illustrate the theoretical results and show the effects of diffusion factors on the time-delay virus model. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
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22 pages, 792 KiB  
Article
Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem
by Yingying Li and Yaxuan Zhang
Axioms 2021, 10(3), 197; https://doi.org/10.3390/axioms10030197 - 23 Aug 2021
Cited by 3 | Viewed by 2506
Abstract
In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms [...] Read more.
In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
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12 pages, 790 KiB  
Article
Global Stability of a Lotka-Volterra Competition-Diffusion-Advection System with Different Positive Diffusion Distributions
by Lili Chen, Shilei Lin and Yanfeng Zhao
Axioms 2021, 10(3), 166; https://doi.org/10.3390/axioms10030166 - 28 Jul 2021
Cited by 2 | Viewed by 2127
Abstract
In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, [...] Read more.
In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
20 pages, 845 KiB  
Article
Delay-Dependent Stability, Integrability and Boundedeness Criteria for Delay Differential Systems
by Osman Tunç, Cemil Tunç and Yuanheng Wang
Axioms 2021, 10(3), 138; https://doi.org/10.3390/axioms10030138 - 29 Jun 2021
Cited by 14 | Viewed by 2211
Abstract
This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov–Krasovskiĭ functional [...] Read more.
This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov–Krasovskiĭ functional (LKF) and using the Lyapunov–Krasovskiĭ method (LKM). Comparisons with a former result that can be found in the literature illustrate the novelty of the stability theorem and show new contributions to the qualitative theory of solutions. A discussion of two illustrative examples and the obtained results are presented. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
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10 pages, 271 KiB  
Article
Generalizations of Hermite–Hadamard Type Integral Inequalities for Convex Functions
by Ying Wu, Hong-Ping Yin and Bai-Ni Guo
Axioms 2021, 10(3), 136; https://doi.org/10.3390/axioms10030136 - 28 Jun 2021
Cited by 5 | Viewed by 2156
Abstract
In the paper, with the help of two known integral identities and by virtue of the classical Hölder integral inequality, the authors establish several new integral inequalities of the Hermite–Hadamard type for convex functions. These newly established inequalities generalize some known results. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
9 pages, 266 KiB  
Article
On Convex F-Contraction in b-Metric Spaces
by Huaping Huang, Zoran D. Mitrović, Kastriot Zoto and Stojan Radenović
Axioms 2021, 10(2), 71; https://doi.org/10.3390/axioms10020071 - 19 Apr 2021
Cited by 10 | Viewed by 2363
Abstract
In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, we give a supportive example to show that our convex F-contraction is quite different from the F [...] Read more.
In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, we give a supportive example to show that our convex F-contraction is quite different from the F-contraction used in the existing literature since our convex F-contraction does not necessarily contain the continuous mapping but the F-contraction contains such mapping. In addition, via some facts, we claim that our results indeed generalize and improve some previous results in the literature. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
17 pages, 289 KiB  
Article
Mann-Type Inertial Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points of Nonexpansive and Quasi-Nonexpansive Mappings
by Lu-Chuan Ceng and Jen-Chih Yao
Axioms 2021, 10(2), 67; https://doi.org/10.3390/axioms10020067 - 19 Apr 2021
Cited by 4 | Viewed by 2008
Abstract
Suppose that in a real Hilbert space H, the variational inequality problem with Lipschitzian and pseudomonotone mapping A and the common fixed-point problem of a finite family of nonexpansive mappings and a quasi-nonexpansive mapping with a demiclosedness property are represented by the [...] Read more.
Suppose that in a real Hilbert space H, the variational inequality problem with Lipschitzian and pseudomonotone mapping A and the common fixed-point problem of a finite family of nonexpansive mappings and a quasi-nonexpansive mapping with a demiclosedness property are represented by the notations VIP and CFPP, respectively. In this article, we suggest two Mann-type inertial subgradient extragradient iterations for finding a common solution of the VIP and CFPP. Our iterative schemes require only calculating one projection onto the feasible set for every iteration, and the strong convergence theorems are established without the assumption of sequentially weak continuity for A. Finally, in order to support the applicability and implementability of our algorithms, we make use of our main results to solve the VIP and CFPP in two illustrating examples. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
19 pages, 558 KiB  
Article
Qualitative Analyses of Integro-Fractional Differential Equations with Caputo Derivatives and Retardations via the Lyapunov–Razumikhin Method
by Osman Tunç, Özkan Atan, Cemil Tunç and Jen-Chih Yao
Axioms 2021, 10(2), 58; https://doi.org/10.3390/axioms10020058 - 9 Apr 2021
Cited by 40 | Viewed by 2923
Abstract
The purpose of this paper is to investigate some qualitative properties of solutions of nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo fractional derivatives. These properties include uniform stability, asymptotic stability, Mittag–Leffer stability and boundedness. The presented results are proved by defining [...] Read more.
The purpose of this paper is to investigate some qualitative properties of solutions of nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo fractional derivatives. These properties include uniform stability, asymptotic stability, Mittag–Leffer stability and boundedness. The presented results are proved by defining an appropriate Lyapunov function and applying the Lyapunov–Razumikhin method (LRM). Hence, some results that are available in the literature are improved for the FrRIDEs and obtained under weaker conditions via the advantage of the LRM. In order to illustrate the results, two examples are provided. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
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