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STUDIA MATHEMATICA - Issue no. 1 / 2007 | |||||||
Article: |
OPTIMAL MULTIVARIATE OSTROWSKI EULER TYPE INEQUALITIES. Authors: GEORGE A. ANASTASSIOU. |
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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 < p < 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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