Superstability of the p-radical sine functional equation

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.

کلیدواژه های Superstability of the p-radical sine functional equation:

Superstability ، p-radical equation ، cosine functional equation ، sine functional equation ، Wilson equation ، Kim equation