Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.9
2.7
Journals
Symmetry
Special Issues
Symmetry, Stability and Sustainability Issues Concerning Derivations
share announcement

Symmetry, Stability and Sustainability Issues Concerning Derivations

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

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 4536

Special Issue Editors

Dr. Zbigniew Lesniak

E-Mail Website
Guest Editor
Mathematics Department, Pedagogical University of Kraków, 30-084 Kraków, Poland
Interests: dynamical systems; functional equations; difference equations; integral equations; stability theory; fixed point theory; numerical analysis; machine learning
Prof. Dr. Janusz Brzdęk

E-Mail Website
Guest Editor
Faculty of Applied Mathematics, AGH University of Science and Technology, Aleja Adama Mickiewicza 30, 30-059 Kraków, Poland
Interests: functional equations and inequalities; Ulam's type stability; fixed point theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ajda Fosner

E-Mail Website
Guest Editor
Faculty of Management, University of Primorska, SI-6104 Koper, Slovenia
Interests: linear algebra; functional analysis; operator theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to focus on the derivations, various generalized notions of derivation, and the problem of their stability in the Ulam sense. Potential topics include properties and applications of different types of derivations (in the broad sense of the notion), including Lie derivation, Jordan derivations, and various characterizations of derivations by means of functional equations.

We also invite contributions related to the concept of Ulam type stability and concerning subjects such as approximate derivations, asymptotically approximate generalized derivations, and various stability, hyperstability, and superstability issues connected with derivations.

The concept of symmetry often plays an important role in the study of derivations, as can be seen, for example, in the case of biderivations and more generally n-derivations defined on various algebraic structures. Moreover, in the stability results, the distances between the approximate solution and the exact solution of the considered equations are mainly measured by functions that are symmetric in some ways.

Dr. Zbigniew Lesniak
Prof. Dr. Janusz Brzdęk
Prof. Dr. Ajda Fosner
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

  • derivations
  • functional equations
  • Ulam type stability
  • fixed point theorems

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

14 pages, 326 KiB  
Article
On Stability of a General n-Linear Functional Equation
by Anna Bahyrycz and Justyna Sikorska
Symmetry 2023, 15(1), 19; https://doi.org/10.3390/sym15010019 - 21 Dec 2022
Cited by 1 | Viewed by 864
Abstract
Let X be a linear space over K∈{R,C}, Y be a real or complex Banach space and f:Xn→Y. With some fixed [...] Read more.
Let X be a linear space over K∈{R,C}, Y be a real or complex Banach space and f:Xn→Y. With some fixed aji,Ci1…in∈K (j∈{1,…,n}, i,ik∈{1,2}, k∈{1,…,n}), we study, using the direct and the fixed point methods, the stability and the general stability of the equation f(a11x11+a12x12,…,an1xn1+an2xn2)=∑1≤i1,…,in≤2Ci1…inf(x1i1,…,xnin), for all xjij∈X (j∈{1,…,n},ij∈{1,2}). Our paper generalizes several known results, among others concerning equations with symmetric coefficients, such as the multi-Cauchy equation or the multi-Jensen equation as well as the multi-Cauchy–Jensen equation. We also prove the hyperstability of the above equation in m-normed spaces with m≥2. Full article
(This article belongs to the Special Issue Symmetry, Stability and Sustainability Issues Concerning Derivations)
16 pages, 283 KiB  
Article
Near-Fixed Point Results via Ƶ-Contractions in Metric Interval and Normed Interval Spaces
by Muhammad Sarwar, Misbah Ullah, Hassen Aydi and Manuel De La Sen
Symmetry 2021, 13(12), 2320; https://doi.org/10.3390/sym13122320 - 04 Dec 2021
Cited by 1 | Viewed by 1230
Abstract
In this paper, using α—admissibility and the concept of simulation functions, some near-fixed point results in the setting of metric interval and normed interval spaces are established. The results have been proved using Z-contractions. Full article
(This article belongs to the Special Issue Symmetry, Stability and Sustainability Issues Concerning Derivations)
19 pages, 362 KiB  
Article
On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey
by Anna Bahyrycz, Janusz Brzdęk, El-sayed El-hady and Zbigniew Leśniak
Symmetry 2021, 13(11), 2200; https://doi.org/10.3390/sym13112200 - 18 Nov 2021
Cited by 10 | Viewed by 1629
Abstract
The theory of Ulam stability was initiated by a problem raised in 1940 by S. Ulam and concerning approximate solutions to the equation of homomorphism in groups. It is somehow connected to various other areas of investigation such as, e.g., optimization and approximation [...] Read more.
The theory of Ulam stability was initiated by a problem raised in 1940 by S. Ulam and concerning approximate solutions to the equation of homomorphism in groups. It is somehow connected to various other areas of investigation such as, e.g., optimization and approximation theory. Its main issue is the error that we make when replacing functions satisfying the equation approximately with exact solutions of the equation. This article is a survey of the published so far results on Ulam stability for functional equations in 2-normed spaces. We present and discuss them, pointing to the various pitfalls they contain and showing possible simple generalizations. In this way, in particular, we demonstrate that the easily noticeable symmetry between them and the analogous results obtained for the classical metric or normed spaces is in fact only apparent. Full article
(This article belongs to the Special Issue Symmetry, Stability and Sustainability Issues Concerning Derivations)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop