Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 3
166
Views
13
CrossRef citations to date
0
Altmetric
Articles

On weighted Ostrowski type, Trapezoid type, Grüss type and Ostrowski–Grüss like inequalities on time scales

, &
Pages 551-571 | Received 05 Jul 2012, Accepted 05 Mar 2013, Published online: 22 Apr 2013

References

  • Hilger S. Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten [Ph.D. thesis]. Würzburg: Universität Würzburg; 1988.
  • Bohner M, Fan M, Zhang JM. Periodicity of scalar dynamic equations and applications to population models. Journal of Mathematical Analysis and Applications. 2007;330:1–9.
  • Atici FM, Biles DC, Lebedinsky A. An application of time scales to economics. Mathematical and Computer Modelling. 2006;43(7–8):718–726.
  • Soria-Hoyo C, Pontiga F, Castellanos A. A PIC based procedure for the integration of multiple time scale problems in gas discharge physics. Journal of Computational Physics. 2009;228:1017–1029.
  • Anastassiou G. Duality principle of time scales and inequalities. Applicable Analysis. 2010;89(12):1837–1854.
  • Bohner M, Matthews T. The Grüss inequality on time scales. Communications in Mathematical Analysis. 2007;3(1):1–8.
  • Bohner M, Matthews T, Tuna A. Diamond-α Grüss type inequalities on time scales. International Journal of Dynamical Systems and Differential Equations. 2011;3(1/2):234–247.
  • Dinu C. Ostrowski type inequalities on time scales. Analele Universitǎţii din Craiova. Seria Matematică-Informatică. 2007;34:43–58.
  • Hussain S, Latif MA, Alomari M. Generalized double-integral Ostrowski type inequalities on time scales. Applied Mathematics Letters. 2011;24(8):1461–1467.
  • Karpuz B, Özkan UM. Generalized Ostrowski’s inequality on time scales. JIPAM Journal of Inequalities in Pure and Applied Mathematics. 2008;9(4):7. Article 112.
  • Li WN. Some delay integral inequalities on time scales. Computers & Mathematics with Applications. 2010;59(6):1929–1936.
  • Li WN, Sheng WH. Some Gronwall type inequalities on time scales. Journal of Mathematical Inequalities. 2010;4(1):67–76.
  • Liu WJ, Ngô QA. An Ostrowski-Grüss type inequality on time scales. Computers & Mathematics with Applications. 2009;58(6):1207–1210.
  • Liu WJ, Ngô QA. A generalization of Ostrowski inequality on time scales for k points. Applied Mathematics and Computation. 2008;203(2):754–760.
  • Liu WJ, Ngô QA, Chen WB. A perturbed Ostrowski-type inequality on time scales for k points for functions whose second derivatives are bounded. Journal of Inequalities and Applications. 2008:12. Art. ID 597241.
  • Liu WJ, Ngô QA, Chen WB. Ostrowski type inequalities on time scales for double integrals. Acta Applicandae Mathematicae. 2010;110(1):477–497.
  • Liu WJ, Ngô QA, Chen WB. A new generalization of Ostrowski type inequality on time scales. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 2009;17(2):101–14.
  • Mir NA, Ullah R. Some inequalities of Ostrowski and Grüss type for triple integrals on time scales. Tamkang Journal of Mathematics. 2011;42(4):415–426.
  • Ngô QA, Liu WJ. A sharp Grüss type inequality on time scales and application to the sharp Ostrowski-Grüss inequality. Communications in Mathematical Analysis. 2009;6(2):33–41.
  • Özkan UM, Sarikaya MZ, Yildirim H. Extensions of certain integral inequalities on time scales. Applied Mathematics Letters. 2008;21(10):993–1000.
  • Özkan UM, Yildirim H. Ostrowski type inequality for double integrals on time scales. Acta Applicandae Mathematicae. 2010;110(1):283–288.
  • Sarikaya MZ. A note on Grüss type inequalities on time scales. Dynamic Systems and Applications. 2008;17(3–4):663–666.
  • Sarikaya MZ. New weighted Ostrowski and Čebyšev type inequalities on time scales. Computers and Mathematics with Applications. 2010;60(5):1510–1514.
  • Sarikaya MZ, Aktan N, Yildirim H. On weighted Čebyšev-Grüss type inequalities on time scales. Journal of Mathematical Inequalities. 2008;2(2):185–195.
  • Sidi Ammi MR, Torres DFM. Combined dynamic Grüss inequalities on time scales. Journal of Mathematical Sciences. 2009;161(6):792–802.
  • Tuna A, Daghan D. Generalization of Ostrowski and Ostrowski-Grüss type inequalities on time scales. Computers and Mathematics with Applications. 2010;60(3):803–811.
  • Tuna A, Yaşar BI, Kutukcu S. A note on integral inequalities involving the product of two functions on time scales. Journal of Applied Functional Analysis. 2008;3(3):341–346.
  • Bohner M, Matthews T. Ostrowski inequalities on time scales. JIPAM Journal of Inequalities in Pure and Applied Mathematics (JIPAM). 2008;9(1):8. Article 6.
  • Dragomir SS. The discrete version of Ostrowski’s inequality in normed linear spaces. JIPAM Journal of Inequalities in Pure and Applied Mathematics. 2002;3(1):16. Article 2.
  • Mitrinović DS, Pečarić JE, Fink AM. Inequalities involving functions and their integrals and derivatives. Dordrecht: Kluwer Academic; 1991.
  • Ostrowski A. Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert. Commentarii Mathematici Helvetici. 1937;10(1):226–227.
  • Wang SF, Xue QL, Liu WJ. Further generalization of Ostrowski–Grüss type inequalities. Advances in Applied Mathematical Analysis. 2008;3(1):17–20.
  • Tseng K-L, Hwang SR, Dragomir SS. Generalizations of weighted Ostrowski type inequalities for mappings of bounded variation and their applications. Computers and Mathematics with Applications. 2008;55(8):1785–1793.
  • Bohner M, Peterson A. Dynamic equations on time scales. Boston (MA): Birkhäuser Boston; 2001.
  • Bohner M, Peterson A. Advances in dynamic equations on time scales. Boston (MA): Birkhäuser Boston; 2003.
  • Lakshmikantham V, Sivasundaram S, Kaymakcalan B. Dynamic systems on measure chains. Dordrecht: Kluwer Academic; 1996.
  • Agarwal R, Bohner M, Peterson A. Inequalities on time scales: a survey. Mathematical Inequalities & Applications. 2001;4(4):535–557.
  • Pachpatte BG. On trapezoid and Grüss-like integral inequalities. Tamkang Journal of Mathematics. 2003;34(4):365–369.
  • Pachpatte BG. New discrete Ostrowski–Grüss like inequalities. Facta Universitatis. Series: Mathematics and Informatics. 2007;22(1):15–20.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.