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Symmetry
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Symmetry in Functional Equations and Inequalities: Volume 2
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Symmetry in Functional Equations and Inequalities: Volume 2

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 10154

Special Issue Editors

Dr. Janusz Brzdek

E-Mail Website
Guest Editor
Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland
Interests: functional equations; inequalities with their applications; functional analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Eliza Jabłonska

E-Mail Website
Guest Editor
Faculty of Mathematics, AGH University of Science and Technology, Kraków, Poland
Interests: mathematical analysis; functional analysis; real analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to attract the leading researchers to submit papers studying problems in Functional Equations and Inequalities (FEI) that involve and/or address various types of symmetry issues. Potential topics include but are not limited to finding solutions to FEI (including difference equations and inequalities) and their properties, the extension of solutions from a restricted domain, separation, various types of stability, convexity, iteration theory, and related subjects (cf., e.g., [1,5,7,8]).

For instance, a kind of symmetry of some functions defining an equation or inequality may be helpful while determining a description of the solutions to it or extending those solutions from a restricted domain. This can be a sort of commutativity in the domain or in the range of a solution, if some inner operations are given there. In Ulam-type stability, we come cross one such situation while considering the stability of the equation of the homomorphism of two semigroups, when the square symmetry of the operation in the domain is sufficient for such stability (under suitable assumptions). Additionally, some types of symmetry (e.g., commutativity) in a semigroup may guarantee the existence of an invariant mean, which is a very efficient tool in proving the stability of several FEI.

In the area of Ulam-type stability, we also encounter another symmetry issue. So far, the distances in this type of stability have been measured mainly by functions that are symmetric in some ways (see [5, 6, 4]). It would be interesting to study such stability problems with these functions not being symmetric, e.g., with quasimetrics, dq-metrics, etc. (for examples of such results, see [2,3]).

We welcome high-quality manuscripts with new result and/or new proofs of already known significant outcomes, as well as outstanding expository papers with sound open problems stated.

References

1 J. Aczél, J. Dhombres, Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications v. 31, Cambridge University Press, 1989.

2 J. Brzdek, El-sayed El-hady, Z. Lesniak, Fixed-point theorem in classes of function with values in a dq-metric space, J. Fixed Point Theory Appl. 20 (2018), 20:143, 16 pp.

3 J. Brzdek, E. Karapınar, A. Petrusel, A fixed point theorem and the Ulam stability in generalized dq-metric spaces, J. Math. Anal. Appl. 467 (2018), 501–520.

4 J. Brzdek, D. Popa, I. Rasa, B. Xu, Ulam Stability of Operators, Mathematical Analysis and its Applications v. 1, Academic Press, Elsevier, Oxford, 2018.

5 D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser Boston, Boston, Mass, USA, 1998.

6 S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York, NY, USA, 2011.

7 M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, 2nd edition (A. Gilányi, ed.), Birkhäuser, Basel, 2009.

8 M. Kuczma, B. Choczewski, R. Ger, Iterative Functional Equations, Cambridge University Press, Cambridge, UK, 1990.

Dr. Janusz Brzdek
Dr. Eliza Jabłonska
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.

Published Papers (8 papers)

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Research

12 pages, 282 KiB  
Article
Some Simpson-like Inequalities Involving the (s,m)-Preinvexity
by Tarek Chiheb, Badreddine Meftah, Abdelkader Moumen, Mouataz Billah Mesmouli and Mohamed Bouye
Symmetry 2023, 15(12), 2178; https://doi.org/10.3390/sym15122178 - 08 Dec 2023
Viewed by 597
Abstract
In this article, closed Newton–Cotes-type symmetrical inequalities involving four-point functions whose second derivatives are (s,m)-preinvex in the second sense are established. Some applications to quadrature formulas as well as inequalities involving special means are provided. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
12 pages, 1258 KiB  
Article
Exact Solutions to Some Nonlinear Time-Fractional Evolution Equations Using the Generalized Kudryashov Method in Mathematical Physics
by Mustafa Ekici
Symmetry 2023, 15(10), 1961; https://doi.org/10.3390/sym15101961 - 23 Oct 2023
Cited by 3 | Viewed by 751
Abstract
In this study, we utilize the potent generalized Kudryashov method to address the intricate obstacles presented by fractional differential equations in the field of mathematical physics. Specifically, our focus centers on obtaining novel exact solutions for three pivotal equations: the time-fractional seventh-order Sawada-Kotera-Ito [...] Read more.
In this study, we utilize the potent generalized Kudryashov method to address the intricate obstacles presented by fractional differential equations in the field of mathematical physics. Specifically, our focus centers on obtaining novel exact solutions for three pivotal equations: the time-fractional seventh-order Sawada-Kotera-Ito equation, the time-fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation, and the time-fractional seventh-order Kaup–Kupershmidt equation. The generalized Kudryashov method, celebrated for its versatility and efficacy in addressing intricate nonlinear problems, plays a central role in our research. This method not only simplifies the equations but also unveils their inner dynamics, rendering them amenable to meticulous analysis. It is worth noting that our fractional derivatives are defined in the context of the conformable fractional derivative, providing a solid foundation for our mathematical investigations. One notable aspect of our study is the visual representation of our findings. Graphical representations of the yielded solutions enliven intricate mathematical structures, providing a concrete insight into the dynamics and behaviors of said equations. This paper highlights the proficiency of the generalized Kudryashov method in resolving complex issues presented by fractional differential equations. Our study not only broadens the range of mathematical methods but also enhances our comprehension of the intriguing realm of nonlinear physical phenomena. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
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14 pages, 358 KiB  
Article
On Ulam Stability with Respect to 2-Norm
by Janusz Brzdęk
Symmetry 2023, 15(9), 1664; https://doi.org/10.3390/sym15091664 - 29 Aug 2023
Cited by 1 | Viewed by 620
Abstract
The Ulam stability of various equations (e.g., differential, difference, integral, and functional) concerns the following issue: how much does an approximate solution of an equation differ from its exact solutions? This paper presents methods that allow to easily obtain numerous general Ulam stability [...] Read more.
The Ulam stability of various equations (e.g., differential, difference, integral, and functional) concerns the following issue: how much does an approximate solution of an equation differ from its exact solutions? This paper presents methods that allow to easily obtain numerous general Ulam stability results with respect to the 2-norms. In four examples, we show how to deduce them from the already known outcomes obtained for classical normed spaces. We also provide some simple consequences of our results. Thus, we demonstrate that there is a significant symmetry between such results in classical normed spaces and in 2-normed spaces. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
28 pages, 436 KiB  
Article
On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey II
by El-sayed El-hady and Janusz Brzdęk
Symmetry 2022, 14(7), 1365; https://doi.org/10.3390/sym14071365 - 02 Jul 2022
Cited by 9 | Viewed by 1195
Abstract
Ulam stability is motivated by the following issue: how much an approximate solution of an equation differs from the exact solutions to the equation. It is connected to some other areas of investigation, e.g., optimization, approximation theory and shadowing. In this paper, we [...] Read more.
Ulam stability is motivated by the following issue: how much an approximate solution of an equation differs from the exact solutions to the equation. It is connected to some other areas of investigation, e.g., optimization, approximation theory and shadowing. In this paper, we present and discuss the published results on such stability for functional equations in the classes of function-taking values in 2-normed spaces. In particular, we point to several pitfalls they contain and provide possible simple improvements to some of them. Thus we show that the easily noticeable symmetry between them and the analogous results proven for normed spaces is, in fact, mainly apparent. Our article complements the earlier similar review published in Symmetry (13(11), 2200) because it concerns the outcomes that have not been discussed in this earlier publication. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
10 pages, 388 KiB  
Article
Novel Mathematical Modelling of Platelet-Poor Plasma Arising in a Blood Coagulation System with the Fractional Caputo–Fabrizio Derivative
by Mohammad Partohaghighi, Ali Akgül, Liliana Guran and Monica-Felicia Bota
Symmetry 2022, 14(6), 1128; https://doi.org/10.3390/sym14061128 - 30 May 2022
Cited by 9 | Viewed by 1245
Abstract
This study develops a fractional model using the Caputo–Fabrizio derivative with order α for platelet-poor plasma arising in a blood coagulation system. The existence of solutions ensures that there are solutions to the considered system of equations. Approximate solutions to the recommended model [...] Read more.
This study develops a fractional model using the Caputo–Fabrizio derivative with order α for platelet-poor plasma arising in a blood coagulation system. The existence of solutions ensures that there are solutions to the considered system of equations. Approximate solutions to the recommended model are presented by selecting different numbers of fractional orders and initial conditions (ICs). For each case, graphs of solutions are supplied through different dimensions. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
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13 pages, 310 KiB  
Article
Estimates for Coefficients of Bi-Univalent Functions Associated with a Fractional q-Difference Operator
by Ebrahim Amini, Shrideh Al-Omari, Kamsing Nonlaopon and Dumitru Baleanu
Symmetry 2022, 14(5), 879; https://doi.org/10.3390/sym14050879 - 25 Apr 2022
Cited by 15 | Viewed by 1535
Abstract
In the present paper, we discuss a class of bi-univalent analytic functions by applying a principle of differential subordinations and convolutions. We also formulate a class of bi-univalent functions influenced by a definition of a fractional q-derivative operator in an open symmetric [...] Read more.
In the present paper, we discuss a class of bi-univalent analytic functions by applying a principle of differential subordinations and convolutions. We also formulate a class of bi-univalent functions influenced by a definition of a fractional q-derivative operator in an open symmetric unit disc. Further, we provide an estimate for the function coefficients |a2| and |a3| of the new classes. Over and above, we study an interesting Fekete–Szego inequality for each function in the newly defined classes. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
12 pages, 1541 KiB  
Article
On a Unique Solution of a Class of Stochastic Predator–Prey Models with Two-Choice Behavior of Predator Animals
by Reny George, Zoran D. Mitrović, Ali Turab, Ana Savić and Wajahat Ali
Symmetry 2022, 14(5), 846; https://doi.org/10.3390/sym14050846 - 19 Apr 2022
Cited by 4 | Viewed by 1780
Abstract
Simple birth–death phenomena are frequently examined in mathematical modeling and probability theory courses since they serve as an excellent foundation for stochastic modeling. Such mechanisms are inherent stochastic extensions of the deterministic population paradigm for population expansion of a particular species in a [...] Read more.
Simple birth–death phenomena are frequently examined in mathematical modeling and probability theory courses since they serve as an excellent foundation for stochastic modeling. Such mechanisms are inherent stochastic extensions of the deterministic population paradigm for population expansion of a particular species in a habitat with constant resource availability and many other organisms. Most animal behavior research differentiates such circumstances into two different events when it comes to two-choice scenarios. On the other hand, in this kind of research, the reward serves a significant role, because, depending on the chosen side and food placement, such situations may be divided into four groups. This article presents a novel stochastic equation that may be used to describe the vast majority of models discussed in the current studies. It is noteworthy that they are connected to the symmetry of the progression of a solution of stochastic equations. The techniques of fixed point theory are employed to explore the existence, uniqueness, and stability of solutions to the proposed functional equation. Additionally, some examples are offered to emphasize the significance of our findings. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
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12 pages, 315 KiB  
Article
Stability of the Equation of q-Wright Affine Functions in Non-Archimedean (n,β)-Banach Spaces
by El-Sayed El-Hady and Iz-iddine El-Fassi
Symmetry 2022, 14(4), 633; https://doi.org/10.3390/sym14040633 - 22 Mar 2022
Cited by 3 | Viewed by 1254
Abstract
In this article, we employ a version of some fixed point theory (FPT) to obtain stability results for the symmetric functional equation (FE) of q-Wright affine functions in non-Archimedean (n,β)-Banach spaces (nArch(n,β) [...] Read more.
In this article, we employ a version of some fixed point theory (FPT) to obtain stability results for the symmetric functional equation (FE) of q-Wright affine functions in non-Archimedean (n,β)-Banach spaces (nArch(n,β)-BS). Furthermore, we give some interesting consequences of our results. In this way, we generalize several earlier outcomes. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities: Volume 2)
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