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A NEW GENERALIZATION OF OSTROWSKI TYPE INEQUALITIES ON ARBITRARY TIME SCALE

Year 2019, Volume: 9 Issue: 2, 172 - 185, 01.06.2019

Abstract

In this paper, a new generalization of Ostrowski type inequalities for twice diferentiable mappings on time scales and some other interesting inequalities as special cases are given.

References

  • Agarwal, R., Bohner, M. and Peterson, A., (2001), Inequalities on time scales: a survey, Math. Inequal. Appl., 4, pp. 535-557.
  • Bohner, M. and Peterson, A., (2001), Dynamic Equations on Time Scales. An Introduction with
  • Applications, Birkh¨auser Boston, Inc., Boston, MA. Bohner, M. and Peterson, A., (2003), Advances in dynamic equations on time scales, Birkh¨auser Boston, Boston, MA.
  • Bohner, M. and Matthews, T., (2008), Ostrowski inequalities on time scales, JIPAM. J. Inequal. Pure Appl. Math., 9, Article 6, 8 pp.
  • Bohner, E. A., Bohner, M. and Matthews, T., (2012), Time scales Ostrowski and Gr¨uss type inequal- ities involving three functions, Nonlinear dynamics and systems theory, vol. 12, no. 2, pp. 119-135.
  • Cerone, P., Dragomir, S. S. and Roumeliotis, J., (1998), An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection 1, 33-39.
  • Dragomir, S.S. and Barnett, N.S., (1998), An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection 1, pp. 69-77.
  • Hilger, S., (1988), Ein Maβkettenkalk¨ul mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis
  • Universit¨at W¨urzburg, W¨urzburg, Germany. Lakshmikantham, V., Sivasundaram, S. and Kaymakcalan, B., (1996), Dynamic systems on measure chains, Mathematics and its Applications, 370, Kluwer Academic Publishers Group, Dordrecht.
  • Liu, W.J., Ngˆo, Q. A. and Chen, W.B., (2009), A new generalization of Ostrowski type inequality on time scales, An. S¸t. Univ. Ovidius Constant¸a, 17, pp. 101-114.
  • Liu, W.J. and Tuna, A., (2012), Weighted Ostrowski, trapezoid and Gr¨uss type inequalities on time scales, J. Math. Inequal., 6, pp. 381-399.
  • Xu, G. and Fang, B. Z., (2016), A New Ostrowski type inequality on time scales, Journal of Mathe- matical Inequalities, Volume 10, Number 3, pp. 751-760.
  • Liu, W. and Tuna, A., (2015), Diamond weighted Ostrowski type and Gr¨uss type inequalities on time scales, Applied Mathematics and Computation, 270, pp. 251-260.
  • Liu, W., Tuna, A. and Jiang, Y., (2014), On weighted Ostrowski type, Trapezoid type, Gr¨uss type and Ostrowski-Gr¨uss like inequalities on time scales, Applicable Analysis, Volume 93, Issue 3, pp. 571.
  • Liu, W., Tuna, A. and Jiang, Y., (2014), New weighted Ostrowski and Ostrowski-Gr¨uss type inequal- ities on time scales, Annals of the Alexandru Ioan Cuza University-Mathematics, Volume LX, Issue , pp. 57-76.
  • Nwaeze, E. R., (2017), A new wei˘ghted Ostrowski type inequality on arbitrary time scale, Journal of
  • King Saud University, Volume 29, Number 1, pp. 230-234. Ostrowski, A., (1937), Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Inte- gralmittelwert, Comment. Math. Helv., 10, pp. 226-227.
  • Pachpatte, B.G., (2004), New inequalities of Ostrowski type for twice differentiable mappings
  • Tamkang Journal of Mathematics, volume 35, number 3, pp. 219-226. Tuna, A. and Daghan, D., (2010), Generalization of Ostrowski and Ostrowski-Gr¨uss type inequalities on time scales, Comput. Math. Appl., 60, pp. 803-811.
  • Tuna, A., Jiang, Y. and Liu, W.J., (2012), Weighted Ostrowski, Ostrowski-Gr¨uss and Ostrowski- ˇ
  • Cebyˇsev Type Inequalities on Time Scales,Publ. Math. Debrecen, 81, pp. 81-102. Tuna, A. and Liu, W., (2016), New weighted ˇCebyˇsev-Ostrowski type integral inequalities on time scales, Journal of Mathematical Inequalities, volume 10, number 2, pp. 327-356, doi:10.7153/jmi-10-27.
Year 2019, Volume: 9 Issue: 2, 172 - 185, 01.06.2019

Abstract

References

  • Agarwal, R., Bohner, M. and Peterson, A., (2001), Inequalities on time scales: a survey, Math. Inequal. Appl., 4, pp. 535-557.
  • Bohner, M. and Peterson, A., (2001), Dynamic Equations on Time Scales. An Introduction with
  • Applications, Birkh¨auser Boston, Inc., Boston, MA. Bohner, M. and Peterson, A., (2003), Advances in dynamic equations on time scales, Birkh¨auser Boston, Boston, MA.
  • Bohner, M. and Matthews, T., (2008), Ostrowski inequalities on time scales, JIPAM. J. Inequal. Pure Appl. Math., 9, Article 6, 8 pp.
  • Bohner, E. A., Bohner, M. and Matthews, T., (2012), Time scales Ostrowski and Gr¨uss type inequal- ities involving three functions, Nonlinear dynamics and systems theory, vol. 12, no. 2, pp. 119-135.
  • Cerone, P., Dragomir, S. S. and Roumeliotis, J., (1998), An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection 1, 33-39.
  • Dragomir, S.S. and Barnett, N.S., (1998), An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection 1, pp. 69-77.
  • Hilger, S., (1988), Ein Maβkettenkalk¨ul mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis
  • Universit¨at W¨urzburg, W¨urzburg, Germany. Lakshmikantham, V., Sivasundaram, S. and Kaymakcalan, B., (1996), Dynamic systems on measure chains, Mathematics and its Applications, 370, Kluwer Academic Publishers Group, Dordrecht.
  • Liu, W.J., Ngˆo, Q. A. and Chen, W.B., (2009), A new generalization of Ostrowski type inequality on time scales, An. S¸t. Univ. Ovidius Constant¸a, 17, pp. 101-114.
  • Liu, W.J. and Tuna, A., (2012), Weighted Ostrowski, trapezoid and Gr¨uss type inequalities on time scales, J. Math. Inequal., 6, pp. 381-399.
  • Xu, G. and Fang, B. Z., (2016), A New Ostrowski type inequality on time scales, Journal of Mathe- matical Inequalities, Volume 10, Number 3, pp. 751-760.
  • Liu, W. and Tuna, A., (2015), Diamond weighted Ostrowski type and Gr¨uss type inequalities on time scales, Applied Mathematics and Computation, 270, pp. 251-260.
  • Liu, W., Tuna, A. and Jiang, Y., (2014), On weighted Ostrowski type, Trapezoid type, Gr¨uss type and Ostrowski-Gr¨uss like inequalities on time scales, Applicable Analysis, Volume 93, Issue 3, pp. 571.
  • Liu, W., Tuna, A. and Jiang, Y., (2014), New weighted Ostrowski and Ostrowski-Gr¨uss type inequal- ities on time scales, Annals of the Alexandru Ioan Cuza University-Mathematics, Volume LX, Issue , pp. 57-76.
  • Nwaeze, E. R., (2017), A new wei˘ghted Ostrowski type inequality on arbitrary time scale, Journal of
  • King Saud University, Volume 29, Number 1, pp. 230-234. Ostrowski, A., (1937), Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Inte- gralmittelwert, Comment. Math. Helv., 10, pp. 226-227.
  • Pachpatte, B.G., (2004), New inequalities of Ostrowski type for twice differentiable mappings
  • Tamkang Journal of Mathematics, volume 35, number 3, pp. 219-226. Tuna, A. and Daghan, D., (2010), Generalization of Ostrowski and Ostrowski-Gr¨uss type inequalities on time scales, Comput. Math. Appl., 60, pp. 803-811.
  • Tuna, A., Jiang, Y. and Liu, W.J., (2012), Weighted Ostrowski, Ostrowski-Gr¨uss and Ostrowski- ˇ
  • Cebyˇsev Type Inequalities on Time Scales,Publ. Math. Debrecen, 81, pp. 81-102. Tuna, A. and Liu, W., (2016), New weighted ˇCebyˇsev-Ostrowski type integral inequalities on time scales, Journal of Mathematical Inequalities, volume 10, number 2, pp. 327-356, doi:10.7153/jmi-10-27.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

A. Tuna This is me

Publication Date June 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 2

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