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http://dx.doi.org/10.4134/BKMS.2008.45.4.763

OSTROWSKI TYPE INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS ON SEGMENTS IN LINEAR SPACES  

Kikianty, Eder (RESEARCH GROUP OF MATHEMATICAL INEQUALITIES AND APPLICATIONS SCHOOL OF ENGINEERING AND SCIENCE VICTORIA UNIVERSITY)
Dragomir, Sever S. (RESEARCH GROUP OF MATHEMATICAL INEQUALITIES AND APPLICATIONS SCHOOL OF ENGINEERING AND SCIENCE VICTORIA UNIVERSITY)
Cerone, Pietro (RESEARCH GROUP OF MATHEMATICAL INEQUALITIES AND APPLICATIONS SCHOOL OF ENGINEERING AND SCIENCE VICTORIA UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 763-780 More about this Journal
Abstract
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.
Keywords
Ostrowski type inequality; absolutely continuous function; semiinner product;
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