Well-Approximable Points for Julia Sets with Parabolic and Critical Points

In this paper we consider rational functions $f\colon \oc \to \oc$ with parabolic and critical points contained in their Julia sets $J(f)$ such that $$ \sum_{n=1}^\infty|(f^n)'(f(c))|^{-1}0 $$ and which are well-approximable by backward iterates of the parabolic periodic points of $f$.