Unicity of meromorphic functions in a certain family

Abstract

Let f and g be two meromorphic functions in family which contain all transcendental meromorphic functions having little poles and zeros. By estimating the zeros of the kth derivative of the function we study the relationship between f and g, and obtain some results which are extensions of some known results. As an application, we prove a uniqueness theorem on meromorphic functions that share three values counting multiplicity.