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(ax2+by2)=af(x)+bf(y),f(ax2+by2)+f(|ax2−by2|)=2a2f(x)+2b2f(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.