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Mathematics
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Quantum Algebras and Operator Theory
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Quantum Algebras and Operator Theory

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

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 8132

Special Issue Editor

Prof. Dr. Jadranka Micic

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia
Interests: operator inequalities; improvements, interpolations and generalizations of general inequalities as well as the applications in functional analysis; norm inequalities; eigenvalue and singularvalue inequalities; quasi-arithmetic operator means; convex function; the various types of convexities

Special Issue Information

Dear Colleagues,

One of the main purposes of research in functional analysis is the theory of inequalities and its integration in contemporary trends in mathematics. The specific objectives are the study of matrix and operator interpretations of real inequalities in various settings, including operator inequalities, norm inequalities, eigenvalue and singular value inequalities, the corresponding refinements and reverses, as well as applications in functional analysis.

It has made significant contributions to science in the theory of inequalities through improvements, interpolations, generalizations of general inequalities, like the Hardy, Hölder, Čebišev, Levinson, and Sherman inequality, the inequalities for means (especially for their converse inequalities), Jensen, and other inequalities for operator convex functions, Cauchy, Kantorovič, Opial, Hilbert, and Grüss inequality, inequalities in n-normalized spaces, integral inequalities, and more.

The notion of convexity is widely spread in almost all branches of mathematics, even in some models in economics, finance, mechanics, and engineering. One of the main goals of the research is the systematic development of the existing theory of convex functions, related generalizations, and applications to operator inequalities. Particular emphasis in the research is placed on the various types of convexities.

Prof. Jadranka Micic
Guest Editor

Manuscript Submission Information

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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

  • operator inequalities
  • matrix inequalities
  • quasi-arithmetic operator means
  • norm inequalities
  • eigenvalue and singularvalue inequalities
  • convex function
  • types of convexities

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Published Papers (3 papers)

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Research

13 pages, 309 KiB  
Article
On Some Recent Results Concerning F-Suzuki-Contractions in b-Metric Spaces
by Ersin Gilić, Diana Dolićanin-Đekić, Zoran D. Mitrović, Dženis Pučić and Hassen Aydi
Mathematics 2020, 8(6), 940; https://doi.org/10.3390/math8060940 - 8 Jun 2020
Cited by 9 | Viewed by 2486
Abstract
The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, [...] Read more.
The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results. Full article
(This article belongs to the Special Issue Quantum Algebras and Operator Theory)
12 pages, 303 KiB  
Article
On Recent Results Concerning F-Contraction in Generalized Metric Spaces
by Jelena Vujaković, Slobodanka Mitrović, Mirjana Pavlović and Stojan Radenović
Mathematics 2020, 8(5), 767; https://doi.org/10.3390/math8050767 - 11 May 2020
Cited by 20 | Viewed by 2585
Abstract
In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using [...] Read more.
In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping. Full article
(This article belongs to the Special Issue Quantum Algebras and Operator Theory)
17 pages, 292 KiB  
Article
On Some New Results in Graphical Rectangular b-Metric Spaces
by Pravin Baradol, Jelena Vujaković, Dhananjay Gopal and Stojan Radenović
Mathematics 2020, 8(4), 488; https://doi.org/10.3390/math8040488 - 1 Apr 2020
Cited by 8 | Viewed by 2352
Abstract
In this paper, we provide an approach to establish the Banach contraction principle (for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results [...] Read more.
In this paper, we provide an approach to establish the Banach contraction principle (for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019). Full article
(This article belongs to the Special Issue Quantum Algebras and Operator Theory)
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