- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 534083, 5 pages
An Opial-Type Inequality on Time Scales
1College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
2Department of Mathematics, The University of Hong Kong, Hong Kong
Received 4 January 2013; Accepted 16 January 2013
Academic Editor: Allan Peterson
Copyright © 2013 Qiao-Luan Li and Wing-Sum Cheung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Z. Opial, “Sur une inégalité,” Annales Polonici Mathematici, vol. 8, pp. 29–32, 1960.
- G. A. Anastassiou, “Opial type inequalities involving Riemann-Liouville fractional derivatives of two functions with applications,” Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 344–374, 2008.
- W.-S. Cheung, Z. Dandan, and J. Pečarić, “Opial-type inequalities for differential operators,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 9, pp. 2028–2039, 2007.
- W. S. Cheung, “Some generalized opial-type inequalities,” Journal of Mathematical Analysis and Applications, vol. 162, no. 2, pp. 317–321, 1991.
- W. S. Cheung, “Opial-type inequalities with functions in variables,” Mathematika, vol. 39, no. 2, pp. 319–326, 1992.
- C.-J. Zhao and W.-S. Cheung, “On some opial-type inequalities,” Journal of Inequalities and Applications, vol. 2011, article 7, 2011.
- C. J. Zhao and W. S. Cheung, “On opial's type inequalities for an integral operator with homogeneous kernel,” Journal of Inequalities and Applications, vol. 2012, article 123, 2012.
- R. P. Agarwal and V. Lakshmikantham, Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations, vol. 6 of Series in Real Analysis, World Scientific Publishing, Singapore, 1993.
- J. D. Li, “Opial-type integral inequalities involving several higher order derivatives,” Journal of Mathematical Analysis and Applications, vol. 167, no. 1, pp. 98–110, 1992.
- R. P. Agarwal and P. Y. H. Pang, Opial Inequalities with Applications in Differential and Difference Equations, vol. 320 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, The Netherlands, 1995.
- D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, vol. 53 of Mathematics and Its Applications (East European Series), Kluwer Academic, Dordrecht, The Netherlands, 1991.
- Z. Olech, “A simple proof of a certain result of Z. Opial,” Annales Polonici Mathematici, vol. 8, pp. 61–63, 1960.
- H. Alzer, “An Opial-type inequality involving higher-order derivatives of two functions,” Applied Mathematics Letters, vol. 10, no. 4, pp. 123–128, 1997.
- R. P. Agarwal and P. Y. H. Pang, “Sharp Opial-type inequalities involving higher order derivatives of two functions,” Mathematische Nachrichten, vol. 174, pp. 5–20, 1995.
- M. Bohner and A. Peterson, Dynamic Equations on Time scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.
- W. N. Li, “Some new dynamic inequalities on time scales,” Journal of Mathematical Analysis and Applications, vol. 319, no. 2, pp. 802–814, 2006.
- M. Bohner and G. Sh. Guseinov, “The convolution on time scales,” Abstract and Applied Analysis, Article ID 58373, 24 pages, 2007.
- C. J. Zhao and W. S. Cheung, “On opial-type inequalities with higher order partial derivatives,” Applied Mathematics Letters, vol. 25, pp. 2156–2161, 2012.