Advances on Nonlinear Functional Analysis

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

Deadline for manuscript submissions: 31 October 2024 | Viewed by 3513

Special Issue Editor


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Guest Editor
Bolyai Institute, University of Szeged, Szegedi Tudományegyetem (SZTE), 6725 Szeged, Hungary
Interests: functional analysis; quantum chemistry

Special Issue Information

Dear Colleagues,

Since the appearance of quantum physics, the importance of investigating infinite dimensional systems and constructing associated algebraic structures has been a constant minor issue, which continuously leads to new branches of research.

Here, we launch a Special Issue on the Mathematics journal platform, titled "Advances on Nonlinear Functional Analysis". See the link below for further information, deadlines, etc.
https://www.mdpi.com/journal/mathematics/special_issues/Nonlinear_Functional_Analysis

For this Special Issue, we are seeking papers concerning manifolds modeled on topological vector spaces, both in real and complex settings, with particular attention to nonlinear flows of endomorphisms subjected to various constrains.

Moreover, we also welcome papers aiming to exhibit relevant applications in physics, ordinary differential equations, partial differential equations, quantum informatics, and other related algebraic topics. These include topological algebras; deformations and infinitesimal methods in topological group and ring theory; vector bundles on surfaces and higher dimensional varieties and their moduli; geometric aspects of numerical algebraic geometry; multilinear algebra and tensor calculus in a nonlinear context; representation toplological groups, rings and algebras with special interest for nonlinear phenomena; quantized function algebras; Lie- and Jordan structures; holomorphic maps of several complex variables and topoloical vector spaces; generalizations of potential theory; complex spaces with a group of automorphisms; the behavior of solutions to functional–differential equations, integral transforms and nonlinear integral equations. Functional analysis for manifolds modeled on topological linear spaces and their applications in quantum physics, biology, and statistics are of particular interest.

Prof. Dr. Laszlo Stacho
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

  • symmetric banach manifolds
  • holomorphic automorphism groups
  • C0-semigroups of holomorphic isometries
  • jordan algebras
  • jordan triples
  • grids associated with jordan structures

Published Papers (4 papers)

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Research

16 pages, 289 KiB  
Article
Lie Modules of Banach Space Nest Algebras
by Pedro Capitão and Lina Oliveira
Mathematics 2024, 12(8), 1251; https://doi.org/10.3390/math12081251 - 20 Apr 2024
Viewed by 371
Abstract
In the present work, we extend to Lie modules of Banach space nest algebras a well-known characterisation of Lie ideals of (Hilbert space) nest algebras. Let A be a Banach space nest algebra and L be a weakly closed Lie A-module. We [...] Read more.
In the present work, we extend to Lie modules of Banach space nest algebras a well-known characterisation of Lie ideals of (Hilbert space) nest algebras. Let A be a Banach space nest algebra and L be a weakly closed Lie A-module. We show that there exist a weakly closed A-bimodule K, a weakly closed subalgebra DK of A, and a largest weakly closed A-bimodule J contained in L,such that JLK+DK, with [K,A]L. The first inclusion holds in general, whilst the second is shown to be valid in a class of nest algebras. Full article
(This article belongs to the Special Issue Advances on Nonlinear Functional Analysis)
13 pages, 322 KiB  
Article
An Alternated Inertial Projection Algorithm for Multi-Valued Variational Inequality and Fixed Point Problems
by Huan Zhang, Xiaolan Liu, Yan Sun and Ju Hu
Mathematics 2023, 11(8), 1850; https://doi.org/10.3390/math11081850 - 13 Apr 2023
Viewed by 792
Abstract
In this paper, we propose an alternated inertial projection algorithm for solving multi-valued variational inequality problem and fixed point problem of demi-contractive mapping. On one hand, this algorithm only requires the mapping is pseudo-monotone. On the other hand, this algorithm is combined with [...] Read more.
In this paper, we propose an alternated inertial projection algorithm for solving multi-valued variational inequality problem and fixed point problem of demi-contractive mapping. On one hand, this algorithm only requires the mapping is pseudo-monotone. On the other hand, this algorithm is combined with the alternated inertial method to accelerate the convergence speed. The global convergence of the algorithm can be obtained under mild conditions. Preliminary numerical results show that the convergence speed of our algorithm is faster than some existing algorithms. Full article
(This article belongs to the Special Issue Advances on Nonlinear Functional Analysis)
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11 pages, 311 KiB  
Article
Compactness in Groups of Group-Valued Mappings
by Diana Caponetti, Alessandro Trombetta and Giulio Trombetta
Mathematics 2022, 10(21), 3973; https://doi.org/10.3390/math10213973 - 26 Oct 2022
Viewed by 734
Abstract
We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness [...] Read more.
We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Fréchet–Šmulian and Ascoli–Arzelà compactness criteria found in the literature. Full article
(This article belongs to the Special Issue Advances on Nonlinear Functional Analysis)
16 pages, 7573 KiB  
Article
New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method
by Xiaomeng Zhu, Jinkang Cheng, Zhuokai Chen and Guojiang Wu
Mathematics 2022, 10(15), 2560; https://doi.org/10.3390/math10152560 - 22 Jul 2022
Cited by 5 | Viewed by 1114
Abstract
In this paper, we use general Riccati equation to construct new solitary wave solutions of the Van der Waals normal form, which is one of the most famous models for natural and industrial granular materials. It is very important to understand the static [...] Read more.
In this paper, we use general Riccati equation to construct new solitary wave solutions of the Van der Waals normal form, which is one of the most famous models for natural and industrial granular materials. It is very important to understand the static and dynamic characteristics of this models in many application fields. We solve the general Riccati equation through different function transformation, and many new hyperbolic function solutions are obtained. Then, it is substituted into the Van der Waals normal form as an auxiliary equation. Abundant types of solitary-wave solutions are obtained by choosing different coefficient in the general Riccati equation, and some of them have not been found in other documents. The results show that the analysis method we used is very simple and effective for dealing with nonlinear models. Full article
(This article belongs to the Special Issue Advances on Nonlinear Functional Analysis)
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