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Axioms
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Operator Theory and Its Applications II
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Operator Theory and Its Applications II

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

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 6787

Special Issue Editors

Prof. Dr. Vladimir Rakocevic

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia
Interests: metric space; fixed point theory; operator theory; summability and matrix transformations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Eberhard Malkowsky

E-Mail Website
Guest Editor
Department of Mathematics, State University Novi Pazar, Vuka Karadžića bb, Novi Pazar 36300, Serbia
Interests: metric space; operator theory; summability and matrix transformations; measures of noncompactness
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This issue is a continuation of the Special Issue “Operator Theory and Its Applications”.

Functional analysis and operator theory are widely used in the description, understanding, and control of dynamical systems and natural processes in physics, chemistry, medicine, and the engineering sciences.

This Special Issue is focused on the most recent advances in operator theory for theoretical and applied sciences arising in all fields of science, engineering applications, and other applied fields. The topics of the Special Issue include but are not limited to:

  • Bounded and unbounded operators between Banach spaces;
  • Matrix transformations on sequence spaces;
  • Fine spectrum;
  • Essential spectrum and Fredholm theory;
  • Measures of noncompactness of operators;
  • Generalized inverses;
  • Operators in fixed point theory;
  • Perov-type contractions.

Prof. Dr. Vladimir Rakocevic
Prof. Dr. Eberhard Malkowsky
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 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.

Published Papers (7 papers)

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Research

11 pages, 277 KiB  
Article
Positive Solutions of Operator Equations AX = B, XC = D
by Haiyan Zhang, Yanni Dou and Weiyan Yu
Axioms 2023, 12(9), 818; https://doi.org/10.3390/axioms12090818 - 25 Aug 2023
Viewed by 663
Abstract
In this paper, using the technique of operator matrix, we consider the positive solution of the system of operator equations AX=B,XC=D in the framework of the Hilbert space; here, the ranges R(A) [...] Read more.
In this paper, using the technique of operator matrix, we consider the positive solution of the system of operator equations AX=B,XC=D in the framework of the Hilbert space; here, the ranges R(A) of A and R(C) of C are not necessarily closed. Firstly, we provide a new necessary and sufficient condition for the existence of positive solutions of AX=B and also provide a representation of positive solutions, which generalize previous conclusions. Furthermore, using the above result, a condition of equivalence for the existence of common positive solutions of AX=B,XC=D is given, as well as the general forms of positive solutions. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
15 pages, 308 KiB  
Article
Further Accurate Numerical Radius Inequalities
by Tariq Qawasmeh, Ahmad Qazza, Raed Hatamleh, Mohammad W. Alomari and Rania Saadeh
Axioms 2023, 12(8), 801; https://doi.org/10.3390/axioms12080801 - 21 Aug 2023
Cited by 3 | Viewed by 788
Abstract
The goal of this study is to refine some numerical radius inequalities in a novel way. The new improvements and refinements purify some famous inequalities pertaining to Hilbert space operators numerical radii. The inequalities that have been demonstrated in this work are not [...] Read more.
The goal of this study is to refine some numerical radius inequalities in a novel way. The new improvements and refinements purify some famous inequalities pertaining to Hilbert space operators numerical radii. The inequalities that have been demonstrated in this work are not only an improvement over old inequalities but also stronger than them. Several examples supporting the validity of our results are provided as well. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
8 pages, 247 KiB  
Article
Unbounded Versions of Two Old Summability Theorems
by Jeff Connor
Axioms 2023, 12(8), 723; https://doi.org/10.3390/axioms12080723 - 26 Jul 2023
Viewed by 498
Abstract
In this note, we obtain extensions of a theorem of Meyer-König and Zeller and a theorem of Wilansky in that the given results do not require a summability matrix to be a bounded operator from the convergent sequences into themselves. The culmination of [...] Read more.
In this note, we obtain extensions of a theorem of Meyer-König and Zeller and a theorem of Wilansky in that the given results do not require a summability matrix to be a bounded operator from the convergent sequences into themselves. The culmination of the results in this note is that a triangle matrix method T with null columns maps a bounded divergent sequence to a null sequence if and only if the range of T is not closed in the null sequences. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
13 pages, 294 KiB  
Article
Generalized Cauchy–Schwarz Inequalities and A-Numerical Radius Applications
by Najla Altwaijry, Kais Feki and Shigeru Furuichi
Axioms 2023, 12(7), 712; https://doi.org/10.3390/axioms12070712 - 22 Jul 2023
Viewed by 883
Abstract
The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which are generalizations of Hilbert spaces. We demonstrate how these new inequalities can be employed to derive novel A-numerical radius inequalities, where A denotes [...] Read more.
The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which are generalizations of Hilbert spaces. We demonstrate how these new inequalities can be employed to derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator in a complex Hilbert space. Some of our novel A-numerical radius inequalities expand upon the existing literature on numerical radius inequalities with Hilbert space operators, which are important tools in functional analysis. We use techniques from semi-Hilbert space theory to prove our results and highlight some applications of our findings. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
9 pages, 304 KiB  
Article
New Results on the Sequence Spaces Inclusion Equations of the Form F⊂E+Fx′ Where F, F′ ∈ {w0, w, w∞}
by Bruno de Malafosse, Eberhard Malkowsky and Vladimir Rakočević
Axioms 2023, 12(7), 683; https://doi.org/10.3390/axioms12070683 - 12 Jul 2023
Viewed by 563
Abstract
We determine the multipliers M(X,Y) where X, Y∈{w0,w,w∞}, and we apply these results to the solvability of both the (SSIE) of the form [...] Read more.
We determine the multipliers M(X,Y) where X, Y∈{w0,w,w∞}, and we apply these results to the solvability of both the (SSIE) of the form F⊂E+wx, where F∈{w0,w,w∞}, and the (SSIE) w⊂E+Wx0 and w⊂E+Wx. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
15 pages, 303 KiB  
Article
New Results on Boas–Bellman-Type Inequalities in Semi-Hilbert Spaces with Applications
by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki
Axioms 2023, 12(7), 638; https://doi.org/10.3390/axioms12070638 - 27 Jun 2023
Cited by 1 | Viewed by 661
Abstract
In this article, we investigate new findings on Boas–Bellman-type inequalities in semi-Hilbert spaces. These spaces are generated by semi-inner products induced by positive and positive semidefinite operators. Our objective is to reveal significant properties of such spaces and apply these results to the [...] Read more.
In this article, we investigate new findings on Boas–Bellman-type inequalities in semi-Hilbert spaces. These spaces are generated by semi-inner products induced by positive and positive semidefinite operators. Our objective is to reveal significant properties of such spaces and apply these results to the field of multivariable operator theory. Specifically, we derive new inequalities that relate to the joint A-numerical radius, the joint operator A-seminorm, and the Euclidean A-seminorm of tuples of semi-Hilbert space operators. We assume that A is a nonzero positive operator. Our discoveries provide insights into the structure of semi-Hilbert spaces and have implications for a broad range of mathematical applications and beyond. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
13 pages, 286 KiB  
Article
New Contributions to Fixed Point Theory for Multi-Valued Feng–Liu Contractions
by Adrian Petruşel, Gabriela Petruşel and Jen-Chih Yao
Axioms 2023, 12(3), 274; https://doi.org/10.3390/axioms12030274 - 06 Mar 2023
Cited by 2 | Viewed by 1149
Abstract
In this paper, we will prove several new results related to the concept of the multi-valued Feng–Liu contraction. An existence, approximation and localization fixed point theorem for a generalized multi-valued nonself Feng–Liu contraction and a new fixed point theorem for multi-valued Feng–Liu contractions [...] Read more.
In this paper, we will prove several new results related to the concept of the multi-valued Feng–Liu contraction. An existence, approximation and localization fixed point theorem for a generalized multi-valued nonself Feng–Liu contraction and a new fixed point theorem for multi-valued Feng–Liu contractions in vector-valued metric spaces are proved. Stability results and an application to a system of operatorial inclusions are also given. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
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