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BOUNDS IN TERMS OF GÂTEAUX DERIVATIVES FOR THE WEIGHTED f-GINI MEAN DIFFERENCE IN LINEAR SPACES

Part of: Communication, information

Published online by Cambridge University Press:  01 April 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: sever.dragomir@vu.edu.au)
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Abstract

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Some bounds in terms of Gâteaux lateral derivatives for the weighted f-Gini mean difference generated by convex and symmetric functions in linear spaces are established. Applications for norms and semi-inner products are also provided.

Keywords

convex functionsJensen’s inequalityGâteaux lateral derivativesnormssemi-inner productsmeansweighted f-Gini mean difference

MSC classification

Secondary: 94A17: Measures of information, entropy
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 420 - 434
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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