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Bounds for the normalised Jensen functional

Published online by Cambridge University Press:  17 April 2009

Sever S. Dragomir
Sever S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University, Melbourne, Vic. 8001, Australia, e-mail: sever@csm.vu.edu.au
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New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon's inequality and the positivity of Kullback-Leibler divergence are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 3 , December 2006 , pp. 471 - 478
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Bullen, P.S., Handbook of mean and their inequalities (Kluwer Academic Publishers, Dordrecht, Boston, London, 2003).CrossRefGoogle Scholar
[2]Cover, T.M. and Thomas, J.A., Elements of information theory (John Wiley and Sons Inc., New York, 1991).Google Scholar
[3]Dragomir, S.S. and Pearce, C.E.M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs (Victoria University, 2000). (ONLINE: http://rgmia. vu. edu. au/monographs).Google Scholar
[4]Kato, M., Saito, K.-S. and Tamura, T., ‘Sharp triangle inequality and its reverse in Banach space’, (submitted).Google Scholar
[5]McEliece, R. J., The theory of information and coding (Addison Wesley Publishing Company, Reading, 1977).Google Scholar
[6]Mitrinović, D.S., Pečarić, J.E. and Fink, A.M., Classical and new inequalities in analysis (Kluwer Academic Publishers, Dordrecht, 1993).CrossRefGoogle Scholar
[7]Pečarić, J.E., Prpschan, F. and Tong, Y.L., Convex functions, partial orderings and statistical applications (Academic Press, Boston, MA, 1992).Google Scholar