Diamond-$α$ Jensen's Inequality on Time Scales

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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-$α$ 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.
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

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Classical Analysis and ODEs, 26D15; 39A13

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http://salesiana.dossiersoluciones.com/handle/123456789/167682

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.1680
 http://arxiv.org/abs/0712.1680
 Journal of Inequalities and Applications, vol. 2008, Article ID 576876, 13 pages, 2008
 doi:10.1155/2008/576876

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arXiv