Year: 2026
Type: article
Abstract: The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there are a lot of open questions. In some specific cases, according to classical results, the unknown additive functions are homomorphisms, derivations, or linear combinations of these. The question arises as to whether the solutions can be described even if the unknown functions are not assumed to be additive but to be generalized monomials. As a starting point, in this paper, we will deal with quadratic functions. We aim to show that quadratic functions that are solutions to certain polynomial equations necessarily have a ‘special’ form. Further, we also present a method to determine these special forms.
Source: Monatshefte für Mathematik
Authors: Eszter Gselmann, Mehak Iqbal
Institution: University of Debrecen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Award: G1967340153
OpenAlex ID: W4392427534