%0 Journal Article
%T Normal Criteria and Shared Values by Differential Polynomials
%A Jihong Wang
%A Qian Lu
%A Qilong Liao
%J Advances in Pure Mathematics
%P 210-217
%@ 2160-0384
%D 2011
%I Scientific Research Publishing
%R 10.4236/apm.2011.14037
%X For a family   of meromorphic functions on a domain D, it is discussed whether  F is normal on D if for every pair functions &lt;i&gt;f&lt;/i&gt;(z),&lt;i&gt;g&lt;/i&gt;﹋&lt;i&gt;F&lt;/i&gt;  ,  &lt;i&gt;f&lt;/i&gt;'每&lt;i&gt;af&lt;/i&gt;&lt;sup&gt;n&lt;/sup&gt;and &lt;i&gt;g&lt;/i&gt;'每&lt;i&gt;ag&lt;/i&gt;&lt;sup&gt;n&lt;/sup&gt;  share value &lt;i&gt;d&lt;/i&gt;  on D when  n=2,3, where &lt;i&gt;a, b&lt;/i&gt; are two complex numbers, &lt;i&gt;a&lt;/i&gt;≧0,﹢,&lt;i&gt;b&lt;/i&gt;≧﹢.Finally, the following result is obtained:Let  &lt;i&gt;F&lt;/i&gt; 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 &lt;i&gt;a&lt;/i&gt;(z)  not idendtically equal to zero, &lt;i&gt;d&lt;/i&gt;(z)  analytic in D, such that for each pair of functions  &lt;i&gt;f&lt;/i&gt; and in &lt;i&gt;F&lt;/i&gt; ,  &lt;i&gt;f&lt;/i&gt;'每&lt;i&gt;a&lt;/i&gt;(z)&lt;i&gt;f&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;  and  &lt;i&gt;g&lt;/i&gt;'每&lt;i&gt;a&lt;/i&gt;(z)&lt;i&gt;g&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;  share the function &lt;i&gt;d&lt;/i&gt;(z) . If &lt;i&gt;a&lt;/i&gt;(z)  has only a multiple zeros and  &lt;i&gt;f&lt;/i&gt;(z)≧﹢ whenever &lt;i&gt;a&lt;/i&gt;(z)=0  , then &lt;i&gt;F&lt;/i&gt;  is normal in D.
%K Normal Family
%K Meromorphic Function
%K Shared Value
%K Differential Polynomial
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=6486