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The system of mixed type additive-quadratic equations and approximations.
- Source :
-
Journal of Inequalities & Applications . 7/25/2024, Vol. 2024 Issue 1, p1-17. 17p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2024
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 178624636
- Full Text :
- https://doi.org/10.1186/s13660-024-03180-8