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Journals
Axioms
Special Issues
New Perspectives in Operator Theory and Functional Analysis
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New Perspectives in Operator Theory and Functional Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 417

Special Issue Editor

Prof. Dr. Chung-Chuan Chen

E-Mail Website
Guest Editor
Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan
Interests: operator theory; functional analysis; abstract harmonic analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Operator theory and functional analysis are important and significant topics in mathematics with various applications in other research areas. Indeed, operator theory includes the general theory of linear operators; special classes of linear operators; individual linear operators as elements of algebraic systems; integral, integrodifferential, and pseudodifferential operators; equations and inequalities involving nonlinear operators and linear spaces; algebras of operators; and so on. Also, functional analysis covers topological linear spaces and related structures for function spaces, normed linear spaces and Banach spaces, inner product spaces and their generalizations, linear function spaces and their duals, topological algebras, normed rings and algebras, Banach algebras for group algebras, and self-adjoint operator algebras.

Through this Special Issue, we expect to collect research papers on the most recent progress, concerns, and questions in this direction. Therefore, we invite researchers to contribute their original and significant research papers which will inspire advances in operator theory and functional analysis.

Prof. Dr. Chung-Chuan Chen
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. 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

  • operator theory
  • functional analysis
  • linear operator
  • nonlinear operator
  • operator algebras

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

Published Papers (2 papers)

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Research

15 pages, 560 KiB  
Article
Characterization Results of Extremization Models with Interval Values
by Savin Treanţă and Omar Mutab Alsalami
Axioms 2025, 14(3), 151; https://doi.org/10.3390/axioms14030151 - 20 Feb 2025
Abstract
The present paper investigates new connections and characterization results on interval-valued minimization models. Specifically, we describe the solution set of the considered control problem with mixed constraints by employing the solution set associated with a class of controlled split variational inequalities. These equivalence [...] Read more.
The present paper investigates new connections and characterization results on interval-valued minimization models. Specifically, we describe the solution set of the considered control problem with mixed constraints by employing the solution set associated with a class of controlled split variational inequalities. These equivalence results are also accompanied by suitable numerical experiments. Full article
(This article belongs to the Special Issue New Perspectives in Operator Theory and Functional Analysis)
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19 pages, 798 KiB  
Article
Multifunctional Expectile Regression Estimation in Volterra Time Series: Application to Financial Risk Management
by Somayah Hussain Alkhaldi, Fatimah Alshahrani, Mohammed Kbiri Alaoui, Ali Laksaci and Mustapha Rachdi
Axioms 2025, 14(2), 147; https://doi.org/10.3390/axioms14020147 - 19 Feb 2025
Abstract
We aim to analyze the dynamics of multiple financial assets with variable volatility. Instead of a standard analysis based on the Black–Scholes model, we proceed with the multidimensional Volterra model, which allows us to treat volatility as a stochastic process. Taking advantage of [...] Read more.
We aim to analyze the dynamics of multiple financial assets with variable volatility. Instead of a standard analysis based on the Black–Scholes model, we proceed with the multidimensional Volterra model, which allows us to treat volatility as a stochastic process. Taking advantage of the long memory function of this type of model, we analyze the reproduced movements using recent algorithms in the field of functional data analysis (FDA). In fact, we develop, in particular, new risk tools based on the asymmetric least squares loss function. We build an estimator using the multifunctional kernel (MK) method and then establish its asymptotic properties. The multidimensionality of the Volterra process is explored through the dispersion component of the convergence rate, while the nonparametric path of the risk tool affects the bias component. An empirical analysis is conducted to demonstrate the ease of implementation of our proposed approach. Additionally, an application on real data is presented to compare the effectiveness of expectile-based measures with Value at Risk (VaR) in financial risk management for multiple assets. Full article
(This article belongs to the Special Issue New Perspectives in Operator Theory and Functional Analysis)
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