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Mathematics
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Advanced Research in Functional Analysis and Operator Theory
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Advanced Research in Functional Analysis and Operator Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 5054

Special Issue Editor

Prof. Dr. Claudio H. Morales

E-Mail Website
Guest Editor
Mathematical Sciences Faculty, University of Alabama in Huntsville, Shelby Center for Science and Technology, Rm 258A, 301 Sparkman Drive Huntsville, Alabama, AL 35899, USA
Interests: geometric fixed point theory in Banach spaces; nonlinear operator theory; differential and integral equations; history and philosophy of mathematics; mathematics education; symbolic logic

Special Issue Information

Dear Colleagues,

This Special Issue focuses on functional analysis, nonlinear operator theory, and its relationship with fixed-point theory, including studies on non-expansive mappings and, more generally, pseudo-contractive operators in Banach spaces; studies on zeros for monotone operators in Hilbert spaces as well as accretive and m-accretive operators in general Banach spaces; studies on the existence and uniqueness types of problems; and studies on the approximation of solutions using iterative methods such as the Mann iteration process. This research component is highly related to the exploration of how mathematics should be learned at the early stages of human life. We welcome the authors of related areas of research, such as partial differential equations, to contribute original research articles to this Special Issue.

Prof. Dr. Claudio H. Morales
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

  • geometric fixed-point theory in Banach spaces
  • nonlinear operator theory
  • differential and integral equations
  • functional analysis

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

17 pages, 320 KiB  
Article
Weyl-Type Theorems of Upper Triangular Relation Matrices
by Yanyan Du and Junjie Huang
Mathematics 2024, 12(23), 3752; https://doi.org/10.3390/math12233752 - 28 Nov 2024
Viewed by 525
Abstract
The spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context [...] Read more.
The spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context of the theory of relations. In this paper, we utilize the connection between linear relations and their induced operators and use space decomposition methods to characterize the distribution of the spectrum for upper triangular relation matrices. We undertake the same for the essential spectrum, Weyl spectrum, and Browder spectrum. Under certain conditions, we obtain a Browder-type theorem and a Weyl-type theorem for such relation matrices. Full article
(This article belongs to the Special Issue Advanced Research in Functional Analysis and Operator Theory)
12 pages, 304 KiB  
Article
Generalizations of Rolle’s Theorem
by Alberto Fiorenza and Renato Fiorenza
Mathematics 2024, 12(14), 2157; https://doi.org/10.3390/math12142157 - 10 Jul 2024
Viewed by 2139
Abstract
The classical Rolle’s theorem establishes the existence of (at least) one zero of the derivative of a continuous one-variable function on a compact interval in the real line, which attains the same value at the extremes, and it is differentiable in the interior [...] Read more.
The classical Rolle’s theorem establishes the existence of (at least) one zero of the derivative of a continuous one-variable function on a compact interval in the real line, which attains the same value at the extremes, and it is differentiable in the interior of the interval. In this paper, we generalize the statement in four ways. First, we provide a version for functions whose domain is in a locally convex topological Hausdorff vector space, which can possibly be infinite-dimensional. Then, we deal with the functions defined in a real interval: we consider the case of unbounded intervals, the case of functions endowed with a weak derivative, and, finally, we consider the case of distributions over an open interval in the real line. Full article
(This article belongs to the Special Issue Advanced Research in Functional Analysis and Operator Theory)
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17 pages, 432 KiB  
Article
Three-Step Iterative Algorithm for the Extended Cayley–Yosida Inclusion Problem in 2-Uniformly Smooth Banach Spaces: Convergence and Stability Analysis
by Imran Ali, Yuanheng Wang and Rais Ahmad
Mathematics 2024, 12(13), 1977; https://doi.org/10.3390/math12131977 - 26 Jun 2024
Viewed by 1760
Abstract
In this article, we investigate and study an extended Cayley–Yosida inclusion problem. We show that our problem is equivalent to a fixed-point equation. Based on the fixed-point equation, we develop a three-step iterative algorithm to solve our problem. Finally, we illustrate the convergence [...] Read more.
In this article, we investigate and study an extended Cayley–Yosida inclusion problem. We show that our problem is equivalent to a fixed-point equation. Based on the fixed-point equation, we develop a three-step iterative algorithm to solve our problem. Finally, we illustrate the convergence of the proposed algorithm with an example, computational table, and convergence graph by using MATLAB 2018b. Full article
(This article belongs to the Special Issue Advanced Research in Functional Analysis and Operator Theory)
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