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Ostrowski type inequality for absolutely continuous functions on segments in linear spaces

Sever S. Dragomir|Eder Kikianty|Pietro Cerone
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회보 (Bulletin of the KMS)|제45권 제4호|pp. 763-780

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키워드

Ostrowski type inequalityabsolutely continuous functionsemi-inner product
주제분류수학

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

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

참고문헌 (28)

  1. C. D. Aliprantis, "Principles of Real Analysis" (1981), North-Holland Publishing Co.
  2. G. A. Anastassiou, "Ostrowski type inequalities", Proceedings of the American Mathematical Society, 123(12), pp.3775~3781 (1995)
  3. N. S. Barnett, "Ostrowski’s inequality for vectorvalued functions and applications", Computers & Mathematics with Applications, 44(5), pp.559~572 (2002)
  4. P. Cerone, "Three point rules in numerical integration", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 47(4), pp.2341~2352 (2001)
  5. P. Cerone, "A new Ostrowski type inequality involving integral means over end intervals", Tamkang Journal of Mathematics, 33(2), pp.109~118 (2002)
  6. P. Cerone, "On relationships between Ostrowski, trapezoidal and Chebychev identities and inequalities", Soochow Journal of Mathematics, 28(3), pp.311~328 (2002)
  7. P. Cerone, "Three point identities and inequalities for n-time differentiable functions", SUT Journal of Mathematics, 36(2), pp.351~383 (2000)
  8. P. Cerone, "On some inequalities arising from Montgomery’s identity (Montgomery’s identity)", Journal of Computational and Applied Mathematics, 5(4), pp.341~367 (2003)
  9. P. Cerone, "Some Ostrowski type inequalities for n-time differentiable mappings and applications", Demonstratio Mathematica, 32(4), pp.697~712 (1999)
  10. S. S. Dragomir, "The Ostrowski integral inequality for mappings of bounded variation", Bulletin of the Australian Mathematical Society, 60(3), pp.495~508 (1999)
  11. and applications in numerical integration, "Journal of Computational and Applied Mathematics", 2001, 343~360
  12. and applications in numerical integration, "Journal of Mathematical Analysis and Applications", 2001, 605~626
  13. S. S. Dragomir, "An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products", Journal of Inequalities in Pure and Applied Mathematics, 3(2), pp.8~ (2002)
  14. S. S. Dragomir, "An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products", Journal of Inequalities in Pure and Applied Mathematics, 3(3), pp.8~ (2002)
  15. S. S. Dragomir, "An Ostrowski like inequality for convex functions and applications", Reviews of Math Computer Software, 16(2), pp.373~382 (2003)
  16. S. S. Dragomir, "Semi-inner Products and Applications" (2004), Nova Science Publishers, Inc.
  17. S. S. Dragomi, "Ostrowski type inequalities for functions defined on linear spaces and applications for semi-inner products", JOURNAL OF CONCRETE AND APPLICABLE MATHEMATICS, 3(1), pp.91~103 (2005)
  18. S. S. Dragomir, "An Ostrowski type inequality for convex functions", Univerzitet u Beogradu. Publikacije Elektrotehni\v ckog Fakulteta. Serija Matematika, 16, pp.12~25 (2005)
  19. S. S. Dragomir, "Generalisations of the Ostrowski Inequality and Applications" (2002), Kluwer Acad. Publ.
  20. C. F. Dunkl, "Mathematical notes: a simple norm inequality", American Mathematical Monthly, 71(1), pp.53~54 (1964)
  21. E. Kikianty, "Sharp inequalities of Ostrowski type for convex functions defined on linear spaces and applications", Computers & Mathematics with Applications
  22. W. A. Kirk, "Mathematical notes: another characterization of inner product spaces", American Mathematical Monthly, 8, pp.890~891 (1964)
  23. P. R. Mercer, "The Dunkl-Williams inequality in an inner product space", MATHEMATICAL INEQUALITIES & APPLICATIONS, 10(2), pp.447~450 (2007)
  24. D. S. Mitrinovi’c, "Inequalities Involving Functions and Their Integrals and Derivatives, Mathematics and its Applications (East European Series), vol. 53" (1991), Kluwer Academic Publishers Group
  25. A. Ostrowski, "¨ Uber die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert", Commentarii Mathematici Helvetici, 10, pp.226~227 (1938)
  26. T. C. Peachey, "The best constant in an inequality of Ostrowski type", Tamkang Journal of Mathematics, 30(3), pp.219~222 (1999)
  27. J. E. Peˇcari’c, "A generalization of Hadamard’s inequality for isotonic linear functionals", Radiation math, 7(1), pp.103~107 (1991)
  28. H. L. Royden, "Real Analysis" (1968), Macmillan Publishing Co. Inc.

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