Symmetry in Mathematical Analysis and Functional Analysis: 3rd Edition

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3103

Special Issue Editors


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Guest Editor
Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania
Interests: Hahn-Banach type theorems; Markov moment problem; polynomial approximation on unbounded subsets; operatorial equations; inequalities
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Special Issue Information

Dear Colleagues,

As we all know, the role and consequences of the notion of symmetry in mathematics and related sciences are very important. In this Special Issue, we want to establish some theoretical results (and their applications) in the fields of mathematical analysis and functional analysis, in which the concept of symmetry plays an essential role. More specifically, we aim to investigate various problems in areas such as optimization problems, polynomial approximation on unbounded subsets, moment problems, variational inequalities, evolutionary problems, dynamical systems, generalized convexity, partial differential equations, and special spaces of self-adjoint operators. Some of these areas of research are strongly intercorrelated. Therefore, we cordially invite you to publish your findings (articles or review papers) on related subjects in this Special Issue.

Prof. Dr. Octav Olteanu
Dr. Savin Treanta
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. Symmetry 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

  • optimization
  • classical and generalized convexity
  • inequalities
  • extension of linear operators
  • sandwich conditions
  • moment problems
  • polynomial approximation
  • Banach lattices
  • self-adjoint operators
  • partial differential equations
  • dynamical systems
  • variational inequalities
  • evolutionary problems

Published Papers (3 papers)

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Research

14 pages, 316 KiB  
Article
Moment Problems and Integral Equations
by Cristian Octav Olteanu
Symmetry 2024, 16(6), 757; https://doi.org/10.3390/sym16060757 - 17 Jun 2024
Viewed by 763
Abstract
The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two [...] Read more.
The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two types of full moment problems are provided. The only given data are the moments of all positive integer orders of the solution and two other linear, not necessarily positive, constraints on it. Under natural assumptions, all the linear solutions are continuous. With their value in the subspace of polynomials being given by the moment conditions, the uniqueness follows. When the involved linear solutions and constraints are positive, the sufficient conditions mentioned above are also necessary. This is achieved in the third part of the paper. All these conditions are written in terms of quadratic expressions. Full article
22 pages, 353 KiB  
Article
pq-Simpson’s Type Inequalities Involving Generalized Convexity and Raina’s Function
by Miguel Vivas-Cortez, Ghulam Murtaza Baig, Muhammad Uzair Awan and Kamel Brahim
Symmetry 2024, 16(4), 457; https://doi.org/10.3390/sym16040457 - 9 Apr 2024
Viewed by 998
Abstract
This study uses Raina’s function to obtain a new coordinated pq-integral identity. Using this identity, we construct several new pq-Simpson’s type inequalities for generalized convex functions on coordinates. Setting p1=p2=1 in these inequalities [...] Read more.
This study uses Raina’s function to obtain a new coordinated pq-integral identity. Using this identity, we construct several new pq-Simpson’s type inequalities for generalized convex functions on coordinates. Setting p1=p2=1 in these inequalities yields well-known quantum Simpson’s type inequalities for coordinated generalized convex functions. Our results have important implications for the creation of post quantum mathematical frameworks. Full article
19 pages, 496 KiB  
Article
On q-Hermite Polynomials with Three Variables: Recurrence Relations, q-Differential Equations, Summation and Operational Formulas
by Mohammed Fadel, Nusrat Raza and Wei-Shih Du
Symmetry 2024, 16(4), 385; https://doi.org/10.3390/sym16040385 - 25 Mar 2024
Cited by 1 | Viewed by 925
Abstract
In the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism. Many properties and new results of q-Hermite polynomials of three variables are established, including [...] Read more.
In the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism. Many properties and new results of q-Hermite polynomials of three variables are established, including their generation function, series description, summation equations, recurrence relationships, q-differential formula and operational rules. Full article
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