A Comparison and Error Analysis of Error Bounds

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A. R. Kashif, T. S. Khan, A. Qayyum, I. Faye, A Comparison and Error Analysis of Error Bounds, Int. J. Anal. Appl., 16 (5) (2018), 751-762.

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A. R. Kashif, T. S. Khan, A. Qayyum, I. Faye

Abstract

In this paper, we present an error analysis with the help of Ostrowski type inequalities for n-times differentiable mappings by using n-times peano kernel. A comparison is also presented which shows that obtained error bounds are better than the previous error bounds.

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References

  1. M. W. Alomari, A companion of ostrowski's inequality for mappings whose first derivatives are bounded and applications numerical integration, Kragujevac J. Math. 36 (2012), 77 - 82.
  2. W. G. Alshanti, A. Qayyum and M. A. Majid, Ostrowski type inequalities by using a generalized quadratic kernel, J. Inequal. Spec. Funct. 8 (4) (2017), 111-135.
  3. W. G. Alshanti and A. Qayyum, A note on new Ostrowski type inequalities using a generalized kernel, Bull. Math. Anal. Appl. 9 (1) (2017), 74-91.
  4. N. S. Barnett, S. S. Dragomir and I. Gomma, A companion for the Ostrowski and the generalized trapezoid inequalities, J. Math. Comput. Model. 50 (2009), 179-187.
  5. H. Budak, M. Z. Sarikaya and A. Qayyum, Improvement in Companion of Ostrowski Type Inequalities for Mappings Whose First Derivatives are of Bounded Variation and Applications, Filomat 31 (2017), 5305-5314.
  6. P. Cerone, S. S. Dragomir, J. Roumeliotis and J. Sunde, A new generalization of the trapezoid formula for n-time differ- entiable mappings and applications, Demonstr. Math. 33(4) (2000), 719-736.
  7. S. S. Dragomir, Some companions of Ostrowski's inequality for absolutely continuous functions and applications, Bull. Korean Math. Soc. 40 (2) (2005), 213-230.
  8. S. S. Dragomir and S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl. 33 (11) (1997), 15-20.
  9. A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Theory, 115 (2) (2002), 260-288.
  10. Z. Liu, Some companions of an Ostrowski type inequality and applications, J. Inequal. Pure Appl. Math. 10 (2) (2009), 10-12.
  11. W. Liu, New Bounds for the Companion of Ostrowski's Inequality and Applications, Filomat, 28 (2014), 167-178.
  12. W. Liu, Y. Zhu and J. Park, Some companions of perturbed Ostrowski-type inequalities based on the quadratic kernel function with three sections and applications, J. Inequal. Appl. 2013 (2013), Article ID 226.
  13. D. S. Mitrinvi ´ c, J. E. Pecari ´ c and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
  14. D. S. Mitrinovi ´ c, J. E. Pecari ´ c and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Math- ematics and its Applications. (East European Series), Kluwer Acadamic Publications Dordrecht, 1991.
  15. A. Ostrowski, ¨ Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralimittelwert, Comment. Math. Hel. 10 (1938), 226-227.
  16. A. Qayyum and S. Hussain, A new generalized Ostrowski Grüss type inequality and applications, Appl. Math. Lett. 25 (2012), 1875-1880.
  17. A. Qayyum, M. Shoaib and I. Faye, Companion of Ostrowski-type inequality based on 5-step quadratic kernel and appli- cations, J. Nonlinear Sci. Appl. 9 (2016), 537-552.
  18. A. Qayyum, M. Shoaib and I. Faye, On new refinements and applications of efficient quadrature rules using n-times differentiable mappings, J. Comput. Anal. Appl. 23 (4) (2017), 723-739.
  19. A. Qayyum, A weighted Ostrowski Grüss Type Inequality for Twice Differentiable Mappings belongs to Lp[a,b] and Ap- plications, The Proceedings of International Conference of Engineering Mathematics, London, U.K., 1-3 July (2009).
  20. N. UJevi ´ c, New bounds for the first inequality of Ostrowski-Grüss type and applications, Comput. Math. Appl. 46 (2003), 421-427.