Inequalities on the Lambert $W$ Function and Hyperpower Function  
  Authors: Abdolhossein Hoorfar, Mehdi Hassani,  
  Keywords: Lambert $W$ function, hyperpower function, special function, inequality.  
  Date Received: 09/04/07  
  Date Accepted: 15/03/08  
  Subject Codes:

33E20, 26D07.

  Editors: Sever S. Dragomir,  

In this note, we obtain inequalities for the Lambert $ W$ function $ W(x)$, defined by $ W(x)e^{W(x)}=x$ for $ xgeq -e^{-1}$. Also, we get upper and lower bounds for the hyperpower function $ h(x)=x^{x^{x^{.^{.^.}}}}$. ;

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