Superstability of the $p$-radical functional equations related to Wilson's and Kim's equation

	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
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
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