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Some New Time Scales Weighted Ostrowski-Grüss Type Inequalities

Yıl 2017, , 626 - 638, 08.12.2017

Adnan Tuna

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

Öz

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.

Anahtar Kelimeler

Ostrowski-Grüss Type Inequalities Time Scales Montgomery Identitiy Time Scales

Kaynakça

  • [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

Yıl 2017, , 626 - 638, 08.12.2017

Adnan Tuna

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

Öz

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

Anahtar Kelimeler

Montgomery Eşitliği Ostrowski-Grüss Tipi Eşitsizlikler Zaman Skalası

Kaynakça

  • [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
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Bölüm Natural Sciences
Yazarlar

Adnan Tuna

Yayımlanma Tarihi 8 Aralık 2017
Gönderilme Tarihi 24 Şubat 2017
Kabul Tarihi 21 Haziran 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

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