Superstability of the $p$-radical sine functional equation
نویسندگان
1 Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2 Department of Mathematics, Kangnam University, Giheung-gu, Yongin-si, Gyeonggi-do, 16979, Repub. of Korea
doi
10.22075/ijnaa.2022.6567چکیده
In this paper, we investigate the transferred superstability of the $p$-radical functional equation \begin{equation*} f\left(\sqrt[p]{\frac{x^{p}+y^{p}}{2}}\right)^{2} -f\left(\sqrt[p]{\frac{x^{p}-y^{p}}{2}}\right)^{2} =f(x)f(y) \end{equation*}with respect to the sine functional quation from the Pexider type $p$-radical functional equation $f\left(\sqrt[p]{x^{p}+y^{p}}\right) +g\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda \cdot h(x)k(y)$, where $p$ is an odd positive integer and $f$ is a complex valued function. Furthermore, the results are applied to the stability of the cosine type $p$-radical functional equations.
