Skip to main content

A Survey of Perturbed Ostrowski Type Inequalities

  • Chapter
  • First Online:
Mathematical Analysis, Approximation Theory and Their Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 111))

  • 1507 Accesses

Abstract

In this paper we survey a number of recent perturbed versions of Ostrowski inequality that have been obtained by the author and provide their connections with numerous classical results of interest.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Apostol, T.M.: Mathematical Analysis, 2nd edn. Addison-Wesley, Reading (1975)

    Google Scholar 

  2. Dragomir, S.S.: On the Ostrowski’s integral inequality for mappings with bounded variation and applications. Math. Inequal. Appl. 4(1), 33–40 (2001). Preprint, RGMIA Res. Rep. Collect. 2(1), Article 7 (1999). http://rgmia.org/papers/v2n1/v2n1-7.pdf

  3. Dragomir, S.S.: A refinement of Ostrowski’s inequality for absolutely continuous functions and applications. Acta Math. Vietnam. 27(2), 203–217 (2002)

    MathSciNet  MATH  Google Scholar 

  4. Dragomir, S.S.: A refinement of Ostrowski’s inequality for absolutely continuous functions whose derivatives belong to \(L_{\infty }\) and applications. Lib. Math. 22, 49–63 (2002)

    MATH  Google Scholar 

  5. Dragomir, S.S.: An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products. J. Inequal. Pure Appl. Math. 3(2), Article 31, 8 pp. (2002)

    Google Scholar 

  6. Dragomir, S.S.: An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products. J. Inequal. Pure Appl. Math. 3(3), Article 35, 8 pp. (2002)

    Google Scholar 

  7. Dragomir, S.S.: Improvements of Ostrowski and generalised trapezoid inequality in terms of the upper and lower bounds of the first derivative. Tamkang J. Math. 34(3), 213–222 (2003)

    MathSciNet  MATH  Google Scholar 

  8. Dragomir, S.S.: Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation. Arch. Math. 91(5), 450–460 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dragomir, S.S.: A functional generalization of Ostrowski inequality via Montgomery identity. Preprint, Acta Math. Univ. Comenian. (2015), 84(1), 63–78. RGMIA Res. Rep. Collect. 16, Article 65, pp. 15 (2013). http://rgmia.org/papers/v16/v16a65.pdf

  10. Dragomir, S.S.: Some perturbed Ostrowski type inequalities for functions of bounded variation. Preprint, Asian-Eur. J. Math. (2015), 8(4), 1550069, pp. 14 RGMIA Res. Rep. Collect. 16, Article 93 (2013). http://rgmia.org/papers/v16/v16a93.pdf

  11. Dragomir, S.S.: Some perturbed Ostrowski type inequalities for absolutely continuous functions (I). Theory Appl. Math. Comput. Sci. (2015), 5(2), 132–147. Preprint, RGMIA Res. Rep. Collect. 16, Article 94 (2013). http://rgmia.org/papers/v16/v16a94.pdf

  12. Dragomir, S.S.: Some perturbed Ostrowski type inequalities for absolutely continuous functions (II). Acta Univ. Apulensis Math. Inform. (43) (2015), 209–228. Preprint, RGMIA Res. Rep. Collect. 16, Article 95 (2013)

    Google Scholar 

  13. Dragomir, S.S.: Some perturbed Ostrowski type inequalities for absolutely continuous functions (III). Transylv. J. Math. Mech. (2015), 7(1), 31–43. Preprint RGMIA Res. Rep. Collect. 16, Article 96 (2013). http://rgmia.org/papers/v16/v16a96.pdf

  14. Dragomir, S.S., Rassias, Th.M. (eds.): Ostrowski Type Inequalities and Applications in Numerical Integration. Springer, Dordrecht (2002). Print ISBN 978-90-481-5990-1

    Google Scholar 

  15. Dragomir, S.S., Wang, S.: A new inequality of Ostrowski’s type in L 1 norm and applications to some special means and to some numerical quadrature rules. Tamkang J. Math. 28, 239–244 (1997)

    MathSciNet  MATH  Google Scholar 

  16. Dragomir, S.S., Wang, S.: A new inequality of Ostrowski’s type in L p norm and applications to some special means and to some numerical quadrature rules. Indian J. Math. 40(3), 299–304 (1998)

    MathSciNet  Google Scholar 

  17. Dragomir, S.S., Wang, S.: Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rules. Appl. Math. Lett. 11(1), 105–109 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fink, A.M.: Bounds on the derivative of a function from its averages. Czechoslov. Math. J. 42(117), 289–310 (1992)

    MathSciNet  MATH  Google Scholar 

  19. Milovanović, G.V., Rassias, M.Th. (eds.): Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York (2014)

    MATH  Google Scholar 

  20. Mitrinović, D.S., Pečarić, J.E., Fink, A.M.: Inequalities for Functions and Their Integrals and Derivatives. Kluwer Academic, Dordrecht (1994)

    MATH  Google Scholar 

  21. Ostrowski, A.: Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv. 10, 226–227 (1938)

    Article  MathSciNet  MATH  Google Scholar 

  22. Peachey, T.C., Mcandrew, A., Dragomir, S.S.: The best constant in an inequality of Ostrowski type. Tamkang J. Math. 30(3), 219–222 (1999)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Dragomir, S.S. (2016). A Survey of Perturbed Ostrowski Type Inequalities. In: Rassias, T., Gupta, V. (eds) Mathematical Analysis, Approximation Theory and Their Applications. Springer Optimization and Its Applications, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-31281-1_8

Download citation

Publish with us

Policies and ethics