The system of mixed type additive-quadratic equations and approximations

Autor: Abasalt Bodaghi, Hesam Mahzoon, Nasser Mikaeilvand
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-17 (2024)
Druh dokumentu: article
ISSN: 1029-242X
92059384
DOI: 10.1186/s13660-024-03180-8
Popis: Abstract In this article, we study the structure of a multiple variable mapping. Indeed, we reduce the system of several mixed additive-quadratic equations defining a multivariable mapping to obtain a single functional equation, say, the multimixed additive-quadratic equation. We also show that such mappings under some conditions can be multi-additive, multi-quadratic and multi-additive-quadratic. Moreover, we establish the Hyers–Ulam stability of the multimixed additive-quadratic equation, using the so-called direct (Hyers) method. Additionally, we present a concrete example (the numerical approximation) regarding the stability of some two variable mappings into real numbers. Applying some characterization results, we indicate two examples for the case that a multimixed additive-quadratic mapping (in the special cases) cannot be stable.
Databáze: Directory of Open Access Journals
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