Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 576876, 13 pages
Research Article

Diamond-α Jensen's Inequality on Time Scales

Moulay Rchid Sidi Ammi, Rui A. C. Ferreira, and Delfim F. M. Torres

Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Received 12 December 2007; Revised 10 February 2008; Accepted 7 April 2008

Academic Editor: Martin Bohner

Copyright © 2008 Moulay Rchid Sidi Ammi et al. 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.


The theory and applications of dynamic derivatives on time scales have recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-α derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen's inequality on time scales via the diamond-α integral and present some corollaries, including Hölder's and Minkowski's diamond-α integral inequalities.