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Mathematics
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Nonlinear Functional Analysis: Theory, Methods, and Applications
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Nonlinear Functional Analysis: Theory, Methods, and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 15 December 2024 | Viewed by 1310

Special Issue Editor

Prof. Dr. Shiqing Zhang

E-Mail Website
Guest Editor
School of Mathematics, Sichuan University, Chengdu 610064, China
Interests: differential equations; nonlinear functional analysis

Special Issue Information

Dear Colleagues,

Nonlinear analysis, especially variational methods, originate from calculus and classical mechanics, so it has a long history, but abstract functional analysis was first used about 100 years ago. Now, abstract nonlinear functional analysis is applied in a wide range of areas. In this Special Issue, we pay attention to the following topics:

  1. Periodic solutions to N-body problems and Hamiltonian systems;
  2. Minimax theory and Ky Fan inequality and applications;
  3. Convex analysis and non-smooth analysis;
  4. Variational methods for ODE and PDE;
  5. Fixed point theory and applications.

Prof. Dr. Shiqing Zhang
Guest Editor

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

  • N-body problems
  • Ky Fan inequality
  • convex analysis
  • non-smooth analysis
  • variational methods

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Published Papers (2 papers)

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Research

10 pages, 223 KiB  
Article
Nash’s Existence Theorem for Non-Compact Strategy Sets
by Xinyu Zhang, Chunyan Yang, Renjie Han and Shiqing Zhang
Mathematics 2024, 12(13), 2017; https://doi.org/10.3390/math12132017 - 28 Jun 2024
Viewed by 351
Abstract
In this paper, we apply the classical FKKM lemma to obtain the Ky Fan minimax inequality defined on nonempty non-compact convex subsets in reflexive Banach spaces, and then we apply it to game theory and obtain Nash’s existence theorem for non-compact strategy sets, [...] Read more.
In this paper, we apply the classical FKKM lemma to obtain the Ky Fan minimax inequality defined on nonempty non-compact convex subsets in reflexive Banach spaces, and then we apply it to game theory and obtain Nash’s existence theorem for non-compact strategy sets, which can be regarded as a new, simple but interesting application of the FKKM lemma and the Ky Fan minimax inequality, and we can also present another proof about the famous John von Neumann’s existence theorem in two-player zero-sum games. Due to the results of Li, Shi and Chang, the coerciveness in the conclusion can be replaced with the P.S. or G.P.S. conditions. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis: Theory, Methods, and Applications)
31 pages, 724 KiB  
Article
Matrix Pencil Optimal Iterative Algorithms and Restarted Versions for Linear Matrix Equation and Pseudoinverse
by Chein-Shan Liu, Chung-Lun Kuo and Chih-Wen Chang
Mathematics 2024, 12(11), 1761; https://doi.org/10.3390/math12111761 - 5 Jun 2024
Viewed by 565
Abstract
We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine the expansion coefficients explicitly, by inverting [...] Read more.
We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine the expansion coefficients explicitly, by inverting an m×m positive definite matrix. The DOIA is a fast, convergent, iterative algorithm. Some properties and the estimation of residual error of the DOIA are given to prove the absolute convergence. Numerical tests demonstrate the usefulness of the double-optimal solution (DOS) and DOIA in solving square or nonsquare linear matrix equations and in inverting nonsingular square matrices. To speed up the convergence, a restarted technique with frequency m is proposed, namely, DOIA(m); it outperforms the DOIA. The pseudoinverse of a rectangular matrix can be sought using the DOIA and DOIA(m). The Moore–Penrose iterative algorithm (MPIA) and MPIA(m) based on the polynomial-type matrix pencil and the optimized hyperpower iterative algorithm OHPIA(m) are developed. They are efficient and accurate iterative methods for finding the pseudoinverse, especially the MPIA(m) and OHPIA(m). Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis: Theory, Methods, and Applications)
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