Diamond-$\alpha$ Jensen's Inequality on Time Scales
Classical Analysis and ODEs
2008-08-27 v3
Abstract
The theory and applications of dynamic derivatives on time scales has 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 H\"{o}lder's and Minkowski's diamond- integral inequalities.
Cite
@article{arxiv.0712.1680,
title = {Diamond-$\alpha$ Jensen's Inequality on Time Scales},
author = {Moulay Rchid Sidi Ammi and Rui A. C. Ferreira and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:0712.1680},
year = {2008}
}
Comments
This is a preprint of an article whose final and definitive form will appear in the \emph{Journal of Inequalities and Applications}, http://www.hindawi.com/journals/jia/. Accepted 07/April/2008