  We derive global curvature estimates for closed strictly star-shaped
(n-2)-convex hypersurfaces in warped product spaces, satisfying the prescribed
(n-2)-curvature equation with a general right-hand side. The proof is
influenced by the recent breakthrough of [Guan-Ren-Wang CPAM 2015] and it can
be readily adapted to establish curvature estimates for semi-convex solutions
to the general k-curvature equation. Furthermore, it can also be used to prove
the same estimates for prescribed curvature measure type equations.
