C-GV triviality of function germs and Newton polyhedra

We provide estimates on the degree of C^l-G_V determinacy (G is one of Mather's groups R or K) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives an explicit order such that the C^l geometrical structure of a function germ is preserved after higher order perturbations, which generalizes the result on C^l-G triviality of function germs given by M.A.S.Ruas.