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  • Research Article
  • Open Access

A Refinement of Jensen's Inequality for a Class of Increasing and Concave Functions

Journal of Inequalities and Applications20082008:717614

https://doi.org/10.1155/2008/717614

  • Received: 23 January 2008
  • Accepted: 9 May 2008
  • Published:

Abstract

Suppose that is strictly increasing, strictly concave, and twice continuously differentiable on a nonempty interval , and is strictly convex on . Suppose that , where , and for , and suppose that . Let , and . We show , , for suitably chosen and . These results can be viewed as a refinement of the Jensen's inequality for the class of functions specified above. Or they can be viewed as a generalization of a refined arithmetic mean-geometric mean inequality introduced by Cartwright and Field in 1978. The strength of the above result is in bringing the variations of the 's into consideration, through .

Keywords

  • Concave Function
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Publisher note

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Authors’ Affiliations

(1)
Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611-6120, USA

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