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

Document Type : Special issue editorial

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Abstract

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.

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