Ostrowski Type Inequality Using Five Step Weighted Kernel

Article Sidebar

PDF
Cite as:
Sofian Obeidat, Muhammad Amer Latif, Ather Qayyum, Ostrowski Type Inequality Using Five Step Weighted Kernel, Int. J. Anal. Appl., 17 (3) (2019), 420-439.

Main Article Content

Sofian Obeidat, Muhammad Amer Latif, Ather Qayyum

Abstract

The purpose of this paper is to establish weighted version of Ostrowski type integral inequalities. The inequalities are obtained by using a newly developed special type of five steps weighted kernel. The introduction of this new Kernel gives some new error bounds for various quadrature rules. Applications for Cumulative Distributive Functions are considered.

Article Details

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. 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.
  3. S.S. Dragomir, Some companions of Ostrowski's inequality for absolutely continuous functions and applications, Bull. Korean Math. Soc. 40(2) (2005), 213-230.
  4. S.S. Dragomir and S. Wang, An inequality of Ostrowski-Gr ¨uss 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.
  5. Z. Liu, Some companions of an Ostrowski type inequality and applications, J. Inequal. Pure Appl. Math. 10(2) (2009), 10-12.
  6. D.S. Mitrinvi ´c, J.E. Pecari ´c and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, (1993).
  7. D.S. Mitrinovi ´c, J.E. Pecari ´c and A.M. Fink, Inequalities involving functions and their integrals and derivatives, Mathematics and its Applications. (East European Series), Kluwer Acadamic Publications Dordrecht, Vol. 53., (1991).
  8. A. Ostrowski, Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralimittelwert ¨ , Comment. Math. Hel. 10 (1938), 226-227.
  9. A. Qayyum and S. Hussain, A new generalized Ostrowski Gr ¨uss type inequality and applications, Appl. Math. Lett. 25 (2012), 1875-1880.
  10. A. Qayyum, M. Shoaib, A.E. Matouk and M.A. Latif, On New Generalized Ostrowski Type Integral inequalities, Abstr. Appl. Anal. 2014 (2014), Art. ID 275806.
  11. A. Qayyum, M. Shoaib and M. A. Latif, A generalized inequality of ostrowski type for twice differentiable bounded mappings and applications, Appl. Math. Sci. 8(38) (2014), 1889-1901.
  12. A. Qayyum, I. Faye, M. Shoaib and M.A. Latif, A Generalization of Ostrowski type inequality for mappings whose second derivatives belong to L1(a, b) and applications, Int. J. Pure Appl. Math. 98(2) (2015), 169-18.
  13. A. Qayyum, M. Shoaib and I. Faye, Some New Generalized Results on Ostrowski Type Integral Inequalities With Application, J. Comput. Anal. Appl. 19(4) (2015), 693-712.
  14. A. Qayyum, M. Shoaib and I. Faye, On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application, Turk. J. Anal. Number Theory, 3(2) (2015), 61-67.
  15. A. Qayyum, M. Shoaib and I. Faye, A Companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications, Filomat, 30(13) (2016), 3601-3614.
  16. N. UJevi ´c, New bounds for the first inequality of Ostrowski-Gr ¨uss type and applications, Comput. Math. Appl. 46 (2003), 421-427.