Approximation of radical functional equations related to quadratic and quartic mappings

In this paper, we introduce and solve of the radical quadratic and radical quartic functional equations: f ( a x 2 + b y 2 ) = a f ( x ) + b f ( y ) , f ( a x 2 + b y 2 ) + f ( | a x 2 − b y 2 | ) = 2 a 2 f ( x ) + 2 b 2 f ( y ) . We also establish some stability results in 2-normed spaces and then the stability by using subadditive and subquadratic functions in p -2-normed spaces for these functional equations.