Weakly Repulsive Fix-Points of Meromorphic Functions and Quasinormal Families

Abstract:

      We study the relationship between the weakly repulsive fixpoints of meromorphic functions and quasinormal families. Let F be a family of meromorphic functions in a domain in D and let q≥ 0 be an integer. We obtain that if for each f ∈F there is an integer k = k (f) > 1 such that the k-th iteration f^k of f has q weakly repulsive fixpoints in D , then F is a quasinormal family with order at most max {4,q+ 2} .