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

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.

Keywords:

stability , Superstability , radical functional equation , cosine functional equation , Wilson functional equation , Kim functional equation