| Autor: |
Hye Jeang Hwang, Gwang Hui Kim |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Electronic Research Archive, Vol 31, Iss 10, Pp 6347-6362 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2688-1594 |
| DOI: |
10.3934/era.2023321https://www.aimspress.com/article/doi/10.3934/era.2023321 |
| Popis: |
In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the $ p $-power-radical functional equation related to sine function equation: $ \begin{equation*} f\left(\sqrt[p]{\frac{x^{p}+y^{p}}{2}}\right)^{2} -f\left(\sqrt[p]{\frac{x^{p}-y^{p}}{2}}\right)^{2} = f(x)f(y) \end{equation*} $ from an approximation of the $ p $-power-radical functional equation: $ \begin{align*} f\left(\sqrt[p]{\frac{x^{p}+y^{p}}{2}}\right)^{2} -f\left(\sqrt[p]{\frac{x^{p}-y^{p}}{2}}\right)^{2} = g(x)h(y), \end{align*} $ where $ p $ is a positive odd integer, and $ f, g $ and $ h $ are complex valued functions on $ \mathbb{R} $. Furthermore, the obtained results are extended to Banach algebras. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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