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arXiv · 0712.1680

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

Moulay Rchid Sidi Ammi·Rui A. C. Ferreira·Delfim F. M. Torres
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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-$α$ 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.

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Moulay Rchid Sidi Ammi, Rui A. C. Ferreira, Delfim F. M. Torres. 2008-04-09. Diamond-$α$ Jensen's Inequality on Time Scales. https://doi.org/10.1155/2008/576876

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