Special Issue "Nonlinear Analysis and Optimization with Applications"

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

Deadline for manuscript submissions: 15 May 2020.

Special Issue Editors

Prof. Dr. Wei-Shih Du
E-Mail Website
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
Special Issues and Collections in MDPI journals
Prof. Dr. Liang-Ju Chu
E-Mail Website
Guest Editor
Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems
Prof. Dr. Fei He
E-Mail Website
Guest Editor
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Prof. Dr. Radu Precup
E-Mail Website
Guest Editor
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj, Romania
Interests: nonlinear boundary value problems for ODEs and PDEs; theory of nonlinear operators; topological fixed point theory; critical point theory; mathematical modeling in biology and medicine
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world.

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:

  • Functional analysis;
  • Critical point theory;
  • Bifurcation theory;
  • Set-valued analysis;
  • Calculus of variations and PDEs;
  • Variational and topological methods for ODEs and PDEs;
  • Fxed point, coincidence point, and best proximity point theory;
  • Nonsmooth analysis and optimization;
  • Graph theory and optimization;
  • Game theory;
  • Convex analysis;
  • Matrix theory;
  • Control theory;
  • Inverse and ill-posed problems;
  • Finite element method;
  • Dynamical systems;
  • Image and signal processing;
  • Data mining

Prof. Dr. Wei-Shih Du
Prof. Dr. Liang-Ju Chu
Prof. Dr. Fei He
Prof. Dr. Radu Precup
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 papers will be 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 quarterly 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 1000 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

  • Functional analysis
  • Critical point theory
  • Bifurcation theory
  • Set-valued analysis
  • ODEs and PDEs
  • Fxed point, coincidence point, and best proximity point theory
  • Nonsmooth analysis
  • Convex analysis
  • Matrix theory
  • Control theory
  • Dynamical systems
  • Image and signal processing
  • Data mining
  • Graph theory and optimization

Published Papers (3 papers)

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Research

Open AccessArticle
Admissible Hybrid Z-Contractions in b-Metric Spaces
Axioms 2020, 9(1), 2; https://doi.org/10.3390/axioms9010002 - 21 Dec 2019
Abstract
In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the [...] Read more.
In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam–Hyers stability of the fixed point problem are also studied. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
Open AccessArticle
Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations
Axioms 2019, 8(4), 134; https://doi.org/10.3390/axioms8040134 - 03 Dec 2019
Abstract
In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling [...] Read more.
In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
Open AccessArticle
Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces
Axioms 2019, 8(4), 121; https://doi.org/10.3390/axioms8040121 - 01 Nov 2019
Abstract
In this paper, we give sufficient conditions to ensure the existence of the best proximity point of monotone relatively nonexpansive mappings defined on partially ordered Banach spaces. An example is given to illustrate our results. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
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