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: 30 November 2024 | Viewed by 14646
Special Issue Editors
Interests: functional equations; inequalities with their applications; functional analysis
Special Issues, Collections and Topics in MDPI journals
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
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