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  Volume 4, Issue 1, Article 21
 
On Entire and Meromorphic Functions that Share Small Functions with their Derivatives
    Authors: Kit-Wing Yu,  
    Keywords: Derivatives, Entire functions, Meromorphic functions, Nevanlinna theory, Sharing values, Small functions.  
    Date Received: 28/02/02  
    Date Accepted: 05/02/03  
    Subject Codes:

30D35

  
    Editors: Hari M. Srivastava,  
 
    Abstract:

In this paper, it is shown that if $f$ is a non-constant entire function, $f$ and $f^{(k)}$ share the small function $a (not equiv 0, infty)$ CM and $delta(0, f)> frac{3}{4}$, then $f equiv f^{(k)}$. Furthermore, if $f$ is non-constant meromorphic, $f$ and $a$ do not have any common pole and $4delta(0, f)+2(8+k)Theta(infty, f)>19+2k$, then the same conclusion can be obtained. Finally, some open questions are posed for the reader.

         
       
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