Normal Criteria and Shared Values by Differential Polynomials
Jihong Wang, Qian Lu, Qilong Liao
DOI: 10.4236/apm.2011.14037   PDF   HTML     3,510 Downloads   7,381 Views   Citations


For a family of meromorphic functions on a domain D, it is discussed whether F is normal on D if for every pair functions f(z),gF , f'–afnand g'–agn share value d on D when n=2,3, where a, b are two complex numbers, a≠0,∞,b≠∞.Finally, the following result is obtained:Let F be a family of meromorphic functions in D, all of whose poles have multiplicity at least 4 , all of whose zeros have multiplicity at least 2. Suppose that there exist two functions a(z) not idendtically equal to zero, d(z) analytic in D, such that for each pair of functions f and in F , f'–a(z)f2 and g'–a(z)g2 share the function d(z) . If a(z) has only a multiple zeros and f(z)≠∞ whenever a(z)=0 , then F is normal in D.

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J. Wang, Q. Lu and Q. Liao, "Normal Criteria and Shared Values by Differential Polynomials," Advances in Pure Mathematics, Vol. 1 No. 4, 2011, pp. 210-217. doi: 10.4236/apm.2011.14037.

Conflicts of Interest

The authors declare no conflicts of interest.


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