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INEQUALITIES IN TERMS OF THE GÂTEAUX DERIVATIVES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

Part of: Inequalities

Published online by Cambridge University Press:  07 February 2011

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

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Some inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.

Keywords

convex functionsGâteaux derivativesJensen’s inequalitynormsmeanf-deviationsf-divergence measures

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 500 - 517
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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