Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T04:21:41.647Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Cerone, P. and Dragomir, S. S., ‘Bounds for the Gini mean difference of an empirical distribution’, Appl. Math. Lett. 19 (2006), 283–293.CrossRefGoogle Scholar
[2]Cerone, P. and Dragomir, S. S., ‘Bounds for the r-weighted Gini mean difference of an empirical distribution’, Math. Comput. Modelling 49(1–2) (2009), 180–188.CrossRefGoogle Scholar
[3]Dragomir, S. S., ‘Inequalities in terms of the Gâteaux derivatives for convex functions in linear spaces with applications’, Bull. Aust. Math. Soc. (2011), doi: 10.1017/S0004972710002054.CrossRefGoogle Scholar
[4]Dragomir, S. S., ‘Some refinements of Jensen’s inequality’, J. Math. Anal. Appl. 168(2) (1992), 518–522.CrossRefGoogle Scholar
[5]Dragomir, S. S., Semiinner Products and Applications (Nova Science Publishers, New York, 2004).Google Scholar
[6]Dragomir, S. S., Discrete Inequalities of the Cauchy–Bunyakovsky–Schwarz Type (Nova Science Publishers, New York, 2004).Google Scholar
[7]Dragomir, S. S., ‘Bounds for the normalised Jensen functional’, Bull. Aust. Math. Soc. 74(3) (2006), 471–478.CrossRefGoogle Scholar
[8]Dragomir, S. S., ‘A refinement of Jensen’s inequality with applications for f-divergence measures’, Taiwanese J. Math. 14(1) (2010), 153–164.CrossRefGoogle Scholar
[9]Dragomir, S. S., ‘Superadditivity of some functionals associated with Jensen’s inequality for convex functions on linear spaces with applications’, Bull. Aust. Math. Soc. 82(1) (2010), 44–61.CrossRefGoogle Scholar
[10]Dragomir, S. S., ‘Weighted f-Gini mean difference for convex and symmetric functions in linear spaces’, Comput. Math. Appl. 60 (2010), 734–743.CrossRefGoogle Scholar
[11]Giorgi, G. M., ‘Bibliographic portrait of the Gini concentration ratio’, Metron 48 (1990), 183–221.Google Scholar
[12]Giorgi, G. M., Il rapporto di concentrazione di Gini, Liberia Editrice Ticci, Siena, 1992.Google Scholar
[13]Koshevoy, G. A. and Mosler, K., ‘Multivariate Gini indices’, J. Multivariate Anal. 60 (1997), 252–276.CrossRefGoogle Scholar