Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 576876, 13 pages
doi:10.1155/2008/576876
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

Recommended by Martin Bohner

Abstract

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.