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Information Journal Paper

Title

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

Pages

  571-582

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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