@article{Hwang2023, 
author = {Hye Jeang Hwang and Gwang Hui Kim},
title = {Superstability of the    p-power-radical functional equation related to sine function equation},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {10},
pages = {6347-6362},
keywords = {stability, superstability, sine functional equation, p-radical functional equation, p-power-radical functional equation},
url = {https://www.sciopen.com/article/10.3934/era.2023321},
doi = {10.3934/era.2023321},
abstract = {In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the    p-power-radical functional equation related to sine function equation:     f            (                                                  x                              p                                      +                          y                              p                                              2                p            )              2        −  f            (                                                  x                              p                                      −                          y                              p                                              2                p            )              2        =  f  (  x  )  f  (  y  )from an approximation of the    p-power-radical functional equation:                       f                              (                                                                                x                                          p                                                        +                                      y                                          p                                                                      2                            p                        )                                2                          −        f                              (                                                                                x                                          p                                                        −                                      y                                          p                                                                      2                            p                        )                                2                          =        g        (        x        )        h        (        y        )        ,            where    p is a positive odd integer, and    f  ,  g and    h are complex valued functions on        R  . Furthermore, the obtained results are extended to Banach algebras.}
}