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    STUDIA MATHEMATICA - Issue no. 1 / 2007  
         
  Article:   OPTIMAL MULTIVARIATE OSTROWSKI EULER TYPE INEQUALITIES.

Authors:  GEORGE A. ANASTASSIOU.
 
       
         
  Abstract:  

In [8] we derived general tight multivariate high order Ostrowski type inequalities for the estimate of the error of a multivariate function f evaluated at a point from its average. The estimates involve only the single partial derivatives of f and are with respect to ||.||p, 1 < < oo. We give here specific applications of these results to the multivariate trapezoid and midpoint rules for functions f differentiable up to order 6. We prove sharpness of these inequalities for differentiation orders m = 1, 2, 4 and with respect to ||.||00.

 
         
     
         
         
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