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ON PERTURBED TRAPEZOIDAL AND MIDPOINT RULES
Pietro Cerone 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
Explicit bounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different. Explicit bounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.
Buse Constantin,Cerone Pietro,Dragomir Sever Silvestru,Roumeliotis John Korean Mathematical Society 2006 대한수학회지 Vol.43 No.5
A refinement of $Gr\ddot{u}ss$ type inequality for the Bochner integral of vector-valued functions in real or complex Hilbert spaces is given. Related results are obtained. Application for finite Fourier transforms of vector-valued functions and some particular inequalities are provided.
Ostrowski type inequality for absolutely continuous functions on segments in linear spaces
Eder Kikianty,Sever S. Dragomir,Pietro Cerone 대한수학회 2008 대한수학회보 Vol.45 No.4
An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp
OSTROWSKI TYPE INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS ON SEGMENTS IN LINEAR SPACES
Kikianty, Eder,Dragomir, Sever S.,Cerone, Pietro Korean Mathematical Society 2008 대한수학회보 Vol.45 No.4
An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.
Constantin Bu\c{s}e,Pietro Cerone,Sever Silvestru Dragomir,John Roumeliotis 대한수학회 2006 대한수학회지 Vol.43 No.5
A refinement of Gr"{u}ss type inequality for the Bochner integral ofvector-valued functions in real or complex Hilbert spaces is given. Relatedresults are obtained. Application for finite Fourier transforms ofvector-valued functions and some particular inequalities are provided.