Author:
G. Yagachitradevi ,S. Lakshminarayanan ,P. Ravindiran
Abstract
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.
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