International Journal of Nonlinear Analysis and Applications

Superstability of the $p$-radical sine functional equation

Document Type : Research Paper

Authors

1 Department of Mathematics, Kangnam University, Giheung-gu, Yongin-si, Gyeonggi-do, 16979, Repub. of Korea

2 Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

Abstract

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. 

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 4
April 2023
Pages 161-170
  • Receive Date: 18 December 2021
  • Revise Date: 29 April 2022
  • Accept Date: 08 May 2022