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Symmetry
Special Issues
Ulam's Type Stability and Symmetries
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Ulam's Type Stability and Symmetries

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

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 3140

Special Issue Editors

Prof. Dr. Dorian Popa

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Guest Editor
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
Interests: ulam stability; functional equations; functional inclusions; differential equations; set-valued analyses
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Liviu Cădariu

E-Mail Website
Guest Editor
Department of Mathematics, Politehnica University of Timișoara, Timișoara, Romania
Interests: Ulam’s type stability of functional equations and integral equations; various methods for proving Ulam’s type stability results (direct and fixed point methods); generalized Hyers–Ulam stability in various spaces (Banach, non-Archimedean and quasi-Banach)
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ioan Rașa

E-Mail Website
Guest Editor
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
Interests: ulam stability of operators; functional equations; functional analysis; approximation theory; inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Issue is mainly devoted to investigations connected with the notion of stability, motivated by the well-known problem of S. Ulam, on the approximate homeomorphisms of metric groups, and related issues. Authors are invited to delivery their contributions on: Ulam’s type stability of functional equations and difference equations, differential equations, integral equations and linear operators, stability of set-valued and iterative functional equations, hyperstability and superstability of functional equations, various methods for proving Ulam’s type stability results, generalized Hyers–Ulam stability, stability on restricted domains and in various (metric, Banach, non-Archimedean, fuzzy, quasi-Banach, etc.) spaces, relations between Ulam’s type stability and fixed point results, its applications and connections to other areas of mathematics (e.g. functional analysis, approximation theory, differential equations, nonlinear analysis).

Prof. Dr. Dorian Popa
Prof. Dr. Liviu Cădariu
Prof. Dr. Ioan Rașa
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

  • Generalized Hyers–Ulam stability of functional equations
  • Ulam’s type stability of difference equations and differential equations
  • Direct method and fixed point method
  • Hyperstability and superstability
  • Ulam’s type stability of integral equations
  • Ulam’s type stability of linear operators
  • Ulam stability in set-valued analysis
  • Best Ulam constant

Published Papers (2 papers)

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Research

9 pages, 248 KiB  
Article
On a Functional Integral Equation
by Daniela Marian, Sorina Anamaria Ciplea and Nicolaie Lungu
Symmetry 2021, 13(8), 1321; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13081321 - 22 Jul 2021
Cited by 9 | Viewed by 1534
Abstract
In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, integral inequalities, monotony and Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential and integral equations and those [...] Read more.
In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, integral inequalities, monotony and Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential and integral equations and those are approached in the stability point of view. In the literature, Fredholm, Volterra and Hammerstein integrals equations with symmetric kernels are studied. Our results can be applied as particular cases to these equations. Full article
(This article belongs to the Special Issue Ulam's Type Stability and Symmetries)
9 pages, 237 KiB  
Article
A C0-Semigroup of Ulam Unstable Operators
by Ana Maria Acu and Ioan Raşa
Symmetry 2020, 12(11), 1844; https://doi.org/10.3390/sym12111844 - 07 Nov 2020
Viewed by 982
Abstract
The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In [...] Read more.
The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t≥0 on C[0,1] such that for each t>0, Rt is Ulam unstable. Moreover, we compute the central moments of Rt and establish a Voronovskaja-type formula. This enables to prove that C2[0,1] is contained in the domain D(A) of the infinitesimal generator of the semigroup. We raise the problem to fully characterize the domain D(A). Full article
(This article belongs to the Special Issue Ulam's Type Stability and Symmetries)
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