JIPAM

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 Cebyšev functional utilising an identity involving a Riemann-Stieltjes integral. A refinement of the classical Cebyšev 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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