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  Volume 7, Issue 2, Article 60
 
On Minkowski and Hardy Integral Inequalities
    Authors: Lazhar Bougoffa,  
    Keywords: Minkowski's inequality, Hardy's inequality.  
    Date Received: 30/11/05  
    Date Accepted: 15/01/06  
    Subject Codes:

26D15.

  
    Editors: Bicheng Yang,  
 
    Abstract:

The reverse Minkowski's integral inequality:

$displaystyle left(int_{a}^{b}f^{p}(x)dx right)^{frac{1}{p}}+left( int_{a}... ...cleft(int_{a}^{b}left(f(x)+g(x) right)^{p}dxright)^{frac{1}{p}}, p>1, $
where $ c$ is a positive constant, and the following Hardy's inequality:
begin{multline*} int_{0}^{infty}left( frac{F_{1}(x)F_{2}(x)cdots F_{i}(x)}... ...left(f_{1}(x)+f_{2}(x)+cdots +f_{i}(x)right)^{p}dx, quad p>1, end{multline*}

where

$displaystyle F_{k}(x)=int_{a}^{x}f_{k}(t)dt,$    where $displaystyle k=1, dots ,i $
are proved.

         
       
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