@article {
author = {Kim, Gwang Hui},
title = {Superstability of the $p$-radical functional equations related to Wilson's and Kim's equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {12},
number = {Special Issue},
pages = {571-582},
year = {2021},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2021.23376.2526},
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.},
keywords = {stability,Superstability,radical functional equation,cosine functional equation,Wilson functional equation,Kim functional equation},
url = {https://ijnaa.semnan.ac.ir/article_5358.html},
eprint = {https://ijnaa.semnan.ac.ir/article_5358_f0cc3d3f37ec8f30cc8ebe601d961302.pdf}
}