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  Volume 3, Issue 5, Article 77
 
New Upper and Lower Bounds for the Cebysev Functional
    Authors: Pietro Cerone, Sever S. Dragomir,  
    Keywords: Cebysev functional, Bounds, Refinement.  
    Date Received: 08/05/02  
    Date Accepted: 05/11/02  
    Subject Codes:

26D15,26D10

  
    Editors: Feng Qi,  
 
    Abstract:

New bounds are developed for the Ceby�ev functional utilising an identity involving a Riemann-Stieltjes integral. A refinement of the classical Ceby�ev inequality is produced for $ f$ monotonic non-decreasing, $ g$ continuous and $ mathcal{M}left( g;t,bright) -mathcal{%% M}left( g;a,tright) geq 0,$ for $ tin left[ a,bright] $ where $ mathcal{%% M}left( g;c,dright) $ is the integral mean over $ left[ c,dright] .$

         
       
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