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Normal Criteria and Shared Values by Differential Polynomials ()

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),*g*∈*F*,*f*'–*af*^{n}and*g*'–*ag*^{n}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)*f*^{2}and*g*'–*a*(z)*g*^{2}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.Share and Cite:

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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