On a General Functional Equation
Year: 2025
Type: article
Abstract: In this paper, we deal with a general functional equation in several variables. We prove the hyperstability of this equation in (m + 1)-normed spaces and describe its general solution in some special cases. In this way, we solve the problems posed by Ciepliński. The considered equation was introduced as a generalization of the equation characterizing n-quadratic functions and has symmetric coefficients (up to sign), and it also generalizes many other known functional equations with symmetric coefficients, such as the multi-Cauchy equation, the multi-Jensen equation, and the multi-Cauchy–Jensen equation. Our results generalize several known results.
Source: Symmetry
DOI: 10.3390/sym17030320
Author: Anna Bahyrycz
Institution: AGH University of Krakow
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4407767282