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The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals

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Abstract

In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. Furthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.

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References

  1. Cheng, X. L.: The Iyengar–Type Inequality. Appl. Math. Lett., 14 (2001), 975–978.

    Article  MathSciNet  Google Scholar 

  2. Dragomir, S. S., Cho, Y. J., Kim, S. S.: Inequalities of Hadamard’s type for Lipschitzian Mappings and their applications. J. Math. Anal. Appl., 245, 489–501 (2000)

    Article  MathSciNet  Google Scholar 

  3. Guessab, A., Schmeisser, G.: Sharp integral inequalities of the Hermite–Hadamard type. J. Approx. Theory, 115, 260–288 (2002)

    Article  MathSciNet  Google Scholar 

  4. Nikolskii, S. M.: Quadrature Formulae, H. M. Stationery Office, London, 1966

  5. Traub, J. F., Wasilkowski, G., Wozniakowski, H.: Information–Based Complexity, Academic Press, New York, 1988

  6. Mitrinović, D. S.: Analytic Inequalities, Springer–Verlag, Berlin–Heidelberg–New York, 1970

  7. Wang C. L., Wang X. H.: On an extension of Hadamard inequalities for convex functions. Chin. Ann. Math., 3, 567–569 (1982)

    Google Scholar 

  8. Vasić, P. M., Lacković, I. B.: On an inequality for convex functions. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 461–497, 63–66 (1974)

  9. Vasić, P. M., Lacković, I. B.: Some complements to the paper: “On an inequality for convex functions”, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 544–576, 59–62 (1976)

  10. Lupas, A.: A generalization of Hadamard inequalities for convex functions. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 544–576, 115–121 (1976)

  11. Wang, C. L., Wang X. H.: Extensions of an Iyengar type inequality. Hangzhou Normal College Natural Science, 3, 25–30 (1980)

    Google Scholar 

  12. Hsu, L. C., Wang, X. H.: Selected topics on methods and examples in mathematical analysis (Chinese), Higher Education Press, Beijing, 1983

  13. Karamata, J.: O prvom stavu srednjih vrednosti odredenih integrala. Glas Srpske Kraljevske Akademije, CLIV Beograd, 119–144 (1933)

  14. Vasić, P. M., Milovanović, G. V.: On an inequality of Iyengar. Univ. Beograd. Publ. Elektrotehn, Fak. Ser. Mat. Fiz., 9(18–24), 544–576 (1976)

    Google Scholar 

  15. Barnett, N. S., Dragomir, S. S.: A perturbed trapezoid inequality in terms of the fourth derivative. Korean J. Comput. & Appl. Math., 9(1), 45–60 (2002)

    MathSciNet  Google Scholar 

  16. Barnett, N. S., Dragomir, S. S.: Bounds in terms of the fourth derivative for the remainder in the corrected trapezoid formula. Computers Math. Applic., 44, 595–605 (2002)

    Article  MathSciNet  Google Scholar 

  17. Barnett, N. S., Dragomir, S. S.: A perturbed trapezoid inequality in terms of the third derivative and applications. Tamkang J. Math., (to appear)

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China

    Xing Hua Wang

  2. College of Mathematics and Information Science, Wenzhou University, Zhejiang 325200, P. R. China

    Xing Hua Wang

  3. Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China

    Shi Jun Yang

  4. Department of Mathematics, Hangzhou Normal College, Hangzhou 310012, P. R. China

    Shi Jun Yang

Authors
  1. Xing Hua Wang
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  2. Shi Jun Yang
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Corresponding author

Correspondence to Xing Hua Wang.

Additional information

This work is supported by the Special Funds for Major State Basic Research Projects (Grant No. G19990328) and National Science Foundation of China (Grant No. 10471128)

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Wang, X.H., Yang, S.J. The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals. Acta Math Sinica 21, 1361–1376 (2005). https://doi.org/10.1007/s10114-005-0578-5

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  • DOI: https://doi.org/10.1007/s10114-005-0578-5

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