NORMAL FAMILIES AND SHARED SETS OF MEROMORPHIC FUNCTIONS

作者：Chen, Jun-Fan^*

来源：Rocky Mountain Journal of Mathematics, 2011, 41(1): 37-43.

DOI：10.1216/RMJ-2011-41-1-37

• Meromorphic function
• normal family
• shared set

Let k, m and n be three positive integers with m >= 2, let F be a family of meromorphic functions in a domain D, all of whose zeros are of multiplicity at least k + 1, and let the sets S(1) = {a(1), a(2), ... , a(m)} and S(2) = {b(1), b(2), ... b(n)} where a(1), a(2), ... a(m) are m distinct finite complex numbers, and b(1), b(2), ..., b(n) are n distinct finite complex numbers. If, for every f is an element of F, f((k))(z) is an element of S(1) double right arrow f(z) is an element of S(2), then,F is normal in D. The condition that the zeros of functions in T are of multiplicity at least k + 1 cannot be weakened, and the corresponding result is no longer true for m = 1.

• 出版日期2011
• 单位福建师范大学