  We consider a convex Euclidean hypersurface that evolves by a volume or area
preserving flow with speed given by a general nonhomogeneous function of the
mean curvature. For a broad class of possible speed functions, we show that any
closed convex hypersurface converges to a round sphere. The proof is based on
the monotonicity of the isoperimetric ratio, which allows to control the inner
and outer radius of the hypersurface and to deduce uniform bounds on the
curvature by maximum principle arguments.
