Mathematica Eterna
Open Access

Abstract

Further result of Schwick normal criterion for families of holomorphic functions

Ming Gao,Xiuqin Li,Wenjun Yuan

In the paper, we prove a result: Let k( 2) be a positive integer and let F be a family of functions holomorphic in a domain D  C and all of whose zeros have multiplicity at least k. Suppose that f(z) and f(k)(z) share zero IM in D for all f 2 F. Then ff0 f : f 2 Fg is normal in D. Our result extend the Schwick [10] normal criteria in which suppose that f(z) and f(k)(z) have no zeros in D for all f 2 F.