대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제45권4호
  • /
  • Pages.763-780
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  • 2008
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2008.11.30
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초록

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.

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참고문헌

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피인용 문헌

  1. Asymptotic expressions for error terms of the perturbed mid-point and trapezoid rules vol.15, pp.6, 2012, https://doi.org/10.1080/09720502.2012.10700811
  2. A Unified Generalization of Perturbed Mid-Point and Trapezoid Inequalities and Asymptotic Expressions for Its Error Term vol.0, pp.0, 2014, https://doi.org/10.2478/aicu-2014-0044