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Some New Time Scales Weighted Ostrowski-Grüss Type Inequalities

Year 2017, Volume: 38 Issue: 4, 626 - 638, 08.12.2017

Adnan Tuna

https://doi.org/10.17776/csj.349330

Abstract

In this paper, we
obtain some new weighted Ostrowski-Grüss type inequalities on time scales. We
also give some other interesting inequalities as special cases.



2010 Mathematics
Subject Classifications : 26D15; 26E70.

Keywords

Ostrowski-Grüss Type Inequalities Time Scales Montgomery Identitiy Time Scales

References

  • [1]. Agarwal R., Bohner M., Peterson A., Inequalities on time scales: a survey, Math. Inequal. Appl., 2001; 4, 535-557.
  • [2]. Bohner M., Peterson A., Dynamic Equations on Time Scales. An Introduction with Applications, Birkhäuser Boston, Inc., Boston, MA, 2001.
  • [3]. Bohner M., Peterson A., Advances in dynamic equations on time scales, Birkhäuser Boston, Boston, MA, 2003.
  • [4]. Bohner M., Matthews T., Ostrowski inequalities on time scales, JIPAM. J. Inequal. Pure Appl. Math., 2008; 9, Article 6, 8 pp.
  • [5]. 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 numarical quadrature rules, Comput. Math. Appl., 1997; 33 (11), pp. 16-20.
  • [6]. Hilger S., Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Würzburg, Germany, 1988.
  • [7]. Lakshmikantham V., Sivasundaram S., Kaymakcalan B., Dynamic systems on measure chains, Mathematics and its Applications, 370, Kluwer Academic Publishers Group, Dordrecht, 1996.
  • [8]. Liu W., Tuna A., Jiang Y., On weighted Ostrowski type, Trapezoid type, Grüss type and Ostrowski-Grüss like inequalities on time scales, Applicable Analysis, 2014; Volume 93, Issue 3, 551-571.
  • [9]. Liu W., Tuna A., Jiang Y., New weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales, Annals of the Alexandru Ioan Cuza University--Mathematics, 2014; Volume LX, Issue 1, 57-76.
  • [10]. Nwaeze E. R., A new weiğhted Ostrowski type inequality on arbitrary time scale, Journal of King Saud University-Science, 2017; volume 29, number 1, pp. 230-234.
  • [11]. Ostrowski A., Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 1937; 10, 226-227.
  • [12]. Tuna A., Daghan D., Generalization of Ostrowski and Ostrowski-Grüss type inequalities on time scales, Comput. Math. Appl., 2010; 60, 803-811.
  • [13]. Tuna A., Jiang Y., Liu W.J., Weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev Type Inequalities on Time Scales, Publ. Math. Debrecen, 2012; 81, 81-10

Zaman Skalasında Bazı Yeni Ağırlıklı Ostrowski-Grüss Tipi Eşitsizlikler

Year 2017, Volume: 38 Issue: 4, 626 - 638, 08.12.2017

Adnan Tuna

https://doi.org/10.17776/csj.349330

Abstract

Bu makalede, zaman skalasında bazı yeni
ağırlıklı Ostrowski-Grüss tipi eşitsizlik elde edilmiştir. Buna ilaveten özel
durumlar olarak bazı diğer ilgili eşitsizlikler verilmiştir.

Keywords

Montgomery Eşitliği Ostrowski-Grüss Tipi Eşitsizlikler Zaman Skalası

References

  • [1]. Agarwal R., Bohner M., Peterson A., Inequalities on time scales: a survey, Math. Inequal. Appl., 2001; 4, 535-557.
  • [2]. Bohner M., Peterson A., Dynamic Equations on Time Scales. An Introduction with Applications, Birkhäuser Boston, Inc., Boston, MA, 2001.
  • [3]. Bohner M., Peterson A., Advances in dynamic equations on time scales, Birkhäuser Boston, Boston, MA, 2003.
  • [4]. Bohner M., Matthews T., Ostrowski inequalities on time scales, JIPAM. J. Inequal. Pure Appl. Math., 2008; 9, Article 6, 8 pp.
  • [5]. 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 numarical quadrature rules, Comput. Math. Appl., 1997; 33 (11), pp. 16-20.
  • [6]. Hilger S., Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Würzburg, Germany, 1988.
  • [7]. Lakshmikantham V., Sivasundaram S., Kaymakcalan B., Dynamic systems on measure chains, Mathematics and its Applications, 370, Kluwer Academic Publishers Group, Dordrecht, 1996.
  • [8]. Liu W., Tuna A., Jiang Y., On weighted Ostrowski type, Trapezoid type, Grüss type and Ostrowski-Grüss like inequalities on time scales, Applicable Analysis, 2014; Volume 93, Issue 3, 551-571.
  • [9]. Liu W., Tuna A., Jiang Y., New weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales, Annals of the Alexandru Ioan Cuza University--Mathematics, 2014; Volume LX, Issue 1, 57-76.
  • [10]. Nwaeze E. R., A new weiğhted Ostrowski type inequality on arbitrary time scale, Journal of King Saud University-Science, 2017; volume 29, number 1, pp. 230-234.
  • [11]. Ostrowski A., Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 1937; 10, 226-227.
  • [12]. Tuna A., Daghan D., Generalization of Ostrowski and Ostrowski-Grüss type inequalities on time scales, Comput. Math. Appl., 2010; 60, 803-811.
  • [13]. Tuna A., Jiang Y., Liu W.J., Weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev Type Inequalities on Time Scales, Publ. Math. Debrecen, 2012; 81, 81-10
There are 13 citations in total.

Details

Journal Section Natural Sciences
Authors

Adnan Tuna

Publication Date December 8, 2017
Submission Date February 24, 2017
Acceptance Date June 21, 2017
Published in Issue Year 2017 Volume: 38 Issue: 4

Cite

APA Tuna, A. (2017). Some New Time Scales Weighted Ostrowski-Grüss Type Inequalities. Cumhuriyet Science Journal, 38(4), 626-638. https://doi.org/10.17776/csj.349330
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