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Superstability of the $p$-radical functional equations related to Wilson's and Kim's equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، Special Issue، اسفند 2021، صفحه 571-582 اصل مقاله (161.15 K) | ||
| نوع مقاله: Special issue editorial | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23376.2526 | ||
| نویسنده | ||
| Gwang Hui Kim* | ||
| Department of Mathematics, Kangnam University, Yongin, Gyeonggi, 16979, Republic of Korea | ||
| تاریخ دریافت: 19 اردیبهشت 1400، تاریخ پذیرش: 23 تیر 1400 | ||
| چکیده | ||
| In this paper, we solve and investigate the superstability of the $p$-radical functional equations related to the following Wilson and Kim functional equations \begin{align*} f\left(\sqrt[p]{x^{p}+y^{p}}\right) &+f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda f(x) g(y),\\ f\left(\sqrt[p]{x^{p}+y^{p}}\right) &+f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda g(x) f(y), \end{align*} where $p$ is an odd positive integer and $f$ is a complex valued function. Furthermore, the results are extended to Banach algebras. | ||
| کلیدواژه‌ها | ||
| stability؛ superstability؛ radical functional equation؛ cosine functional equation؛ Wilson functional equation؛ Kim functional equation | ||
| مراجع | ||
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