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Diamond- Jensen's Inequality on Time Scales

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.

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Correspondence to Delfim F. M. Torres.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sidi Ammi, M.R., Ferreira, R.A.C. & Torres, D.F.M. Diamond- Jensen's Inequality on Time Scales. J Inequal Appl 2008, 576876 (2008). https://doi.org/10.1155/2008/576876

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

Keywords

  • Linear Combination
  • Basic Property
  • Generalize Version
  • Full Article
  • Integral Inequality