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Diamond-α Jensen's inequality on time scales

By M.R. Sidi Ammi, R.A.C. Ferreira and D.F.M. Torres

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. Copyright © 2008 Moulay Rchid Sidi Ammi et al

Publisher: Hindawi Publishing Corporation
Year: 2008
DOI identifier: 10.1155/2008
OAI identifier: oai:ria.ua.pt:10773/4092
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