2-Banach stability results for the radical cubic functional equation related to quadratic mapping

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation f ( 3 √ ax3 + by3 ) + f (3 √ ax3 − by3 ) = 2a² f (x) + 2b² f (y), x, y ∈ R, for a mapping f from R into a vector space. We also investigate some stability and hyperstability results for the considered equation in 2-Banach spaces by using an analogue theorem of Brzdek in [17].