Normality and repelling periodic points

Let k ≥ 3(≥ 2) be an integer and F be a family of functions meromorphic in a domain D ⊂ C, all of whose poles have multiplicity at least 2 (at least 3). If in D each f ∈ F has neither repelling fixed points nor repelling periodic points of period k, then F is a normal family in D. Examples are given to show that the conditions on poles are necessary and sharp.