Generalized Hyers-Ulam stability of a 3D additive-quadratic functional equation in Banach spaces: A study with counterexamples
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DOI:
https://doi.org/10.26637/mjm1104/007Abstract
In this research, we focus on solving a mixed type additive-quadratic functional equation expressed as:
\begin{align*}
&h(3s_1+2s_2+s_3) + h(3s_1+2s_2-s_3) + h(3s_1-2s_2+s_3)\\+&h(3s_1-2s_2-s_3)=12\tilde{h}(s_1) +8\tilde{h}(s_2)+2\tilde{h}(s_3)+12h(s_1)
\end{align*}
where \(\tilde{h}(s_1)=h(s_1)+h(-s_1)\) is derived. We proceed to investigate the generalized Hyers-Ulam stability of this equation within the framework of Banach spaces, employing the Hyers direct method. Additionally, examples of non-stable cases are also provided.
Keywords:
Additive-Quadratic functional equations, Direct method, Generalized Hyers-Ulam stability, Ulam stability, Banach spaceMathematics Subject Classification:
39B52, 39B72, 39B82- Pages: 417-446
- Date Published: 01-10-2023
- Vol. 11 No. 04 (2023): Malaya Journal of Matematik (MJM)
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