Open Access

Diamond- Jensen's Inequality on Time Scales

  • Moulay Rchid Sidi Ammi1,
  • Rui A. C. Ferreira1 and
  • Delfim F. M. Torres1Email author
Journal of Inequalities and Applications20082008:576876

https://doi.org/10.1155/2008/576876

Received: 12 December 2007

Accepted: 7 April 2008

Published: 14 April 2008

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- 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- integral and present some corollaries, including Hölder's and Minkowski's diamond- integral inequalities.

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Mathematics, University of Aveiro

Copyright

© Moulay Rchid Sidi Ammi et al. 2008

This article is published under license to BioMed Central Ltd. 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.