A recent article Li and Lv considered contraction of convex hypersurfaces by
certain nonhomogeneous functions of curvature, showing convergence to points in
finite time in certain cases where the speed is a function of a degree-one
homogeneous, concave and inverse concave function of the principle curvatures.
In this article we extend the result to various other cases that are analogous
to those considered in other earlier work, and we show that in all cases, where
sufficient pinching conditions are assumed on the initial hypersurface, then
under suitable rescaling the final point is asymptotically round and
convergence is exponential in the $C^\infty$-topology.