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A NEW GENERALIZATION OF OSTROWSKI TYPE INEQUALITIES ON ARBITRARY TIME SCALE

Yıl 2019, Cilt: 9 Sayı: 2, 172 - 185, 01.06.2019

Öz

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.

Kaynakça

  • 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.
Yıl 2019, Cilt: 9 Sayı: 2, 172 - 185, 01.06.2019

Öz

Kaynakça

  • 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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

A. Tuna Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 2

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