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SOME REVERSES OF THE JENSEN INEQUALITY WITH APPLICATIONS

Published online by Cambridge University Press:  07 February 2013

S. S. DRAGOMIR
S. S. DRAGOMIR*
Affiliation:
Mathematics, School of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia email [email protected] School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa email [email protected]
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Abstract

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Two new reverses of the celebrated Jensen’s inequality for convex functions in the general setting of the Lebesgue integral, with applications to means, Hölder’s inequality and $f$-divergence measures in information theory, are given.

Keywords

Jensen’s inequalityHölder’s inequalitymeasurable functionsLebesgue integraldivergence measuresf-divergence measures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 177 - 194
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

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