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Superstability of the $p$-radical sine functional equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 14، دوره 14، شماره 4، تیر 2023، صفحه 161-170 اصل مقاله (424.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6567 | ||
| نویسندگان | ||
| Gwang Hui Kim* 1؛ Madjid Eshaghi Gordji2 | ||
| 1Department of Mathematics, Kangnam University, Giheung-gu, Yongin-si, Gyeonggi-do, 16979, Repub. of Korea | ||
| 2Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran | ||
| تاریخ دریافت: 27 آذر 1400، تاریخ بازنگری: 09 اردیبهشت 1401، تاریخ پذیرش: 18 اردیبهشت 1401 | ||
| چکیده | ||
| In this paper, we investigate the transferred superstability of the $p$-radical functional 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*} with respect to the sine functional quation from the Pexider type $p$-radical functional equation $f\left(\sqrt[p]{x^{p}+y^{p}}\right) +g\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda \cdot h(x)k(y)$, where $p$ is an odd positive integer and $f$ is a complex valued function. Furthermore, the results are applied to the stability of the cosine type $p$-radical functional equations. | ||
| کلیدواژه‌ها | ||
| superstability؛ $p$-radical equation؛ cosine functional equation؛ sine functional equation؛ Wilson equation؛ Kim equation | ||
| مراجع | ||
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