V-bilipschitz determinacy of weighted homogeneous analytic function-germs on weighted homogeneous real analytic varieties

In this article, we provide estimates for the degree of V-bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Łojasiewicz condition. The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.