Journal of Applied Mathematics and Computing

, Volume 32, Issue 1, pp 157–169 | Cite as

New generalization of perturbed Ostrowski type inequalities and applications

Article

Abstract

Generalizations of perturbed Ostrowski type inequality for functions of Lipschitzian type are established. Applications in numerical integration and cumulative distribution functions are also given.

Keywords

Ostrowski type inequality Function of Lipschitzian type Numerical integration Cumulative distribution functions 

Mathematics Subject Classification (2000)

26D10 41A55 65D30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barnett, N.S., Dragomir, S.S.: Some inequalities for probability, expectation and variance of random variable defined over a finite interval. Comput. Math. Appl. 43, 1319–1357 (2002) MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cerone, P., Dragomir, S.S.: Trapezoidal-type rules from an inequalities point of view. In: Anastassiou, G. (ed.) Handbook of Analytic-Computational Methods in Applied Mathematics, pp. 65–134. CRC Press, New York (2000) Google Scholar
  3. 3.
    Cerone, P., Dragomir, S.S.: Midpoint-type rules from an inequalities point of view. In: Anastassiou, G. (ed.) Handbook of Analytic-Computational Methods in Applied Mathematics, pp. 65–134. CRC Press, New York (2000) Google Scholar
  4. 4.
    Dragomir, S.S., Agarwal, R.P., Cerone, P.: On Simpson’s inequality and applications. J. Inequal. Appl. 5, 533–579 (2000) MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Dragomir, S.S., Cerone, P., Roumeliotis, J.: A new generalization of Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means. Appl. Math. Lett. 13(1), 19–25 (2000) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Liu, W.J., Xue, Q.L., Wang, S.F.: Several new perturbed Ostrowski-like type inequalities. J. Inequal. Pure Appl. Math. 8(4), 110 (2007) MathSciNetGoogle Scholar
  7. 7.
    Liu, W.J., Li, C.C., Hao, Y.M.: Further generalization of some double integral inequalities and applications. Acta Math. Univ. Comen. 77(1), 147–154 (2008) MATHMathSciNetGoogle Scholar
  8. 8.
    Liu, Z.: Some Ostrowski-Grüss type inequalities and applications. Comput. Math. Appl. 53, 73–79 (2007) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Liu, Z.: Some inequalities of Ostrowski type and applications. Appl. Math. E-Notes 7, 93–101 (2007) MATHMathSciNetGoogle Scholar
  10. 10.
    Ujević, N.: Perturbations of an Ostrowski type inequality and applications. Int. J. Math. Math. Sci. 32(8), 491–500 (2002) MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ujević, N.: A generalization of Ostrowski’s inequality and applications in numerical integration. Appl. Math. Lett. 17, 133–137 (2004) MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Ujević, N.: Error inequalities for a generalized trapezoid rule. Appl. Math. Lett. 19, 32–37 (2006) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2009

Authors and Affiliations

  1. 1.College of Mathematics and PhysicsNanjing University of Information Science and TechnologyNanjingChina

Personalised recommendations