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INEQUALITIES FOR SUPERADDITIVE FUNCTIONALS WITH APPLICATIONS

Part of: Inequalities Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  01 June 2008

SEVER S. DRAGOMIR
SEVER S. DRAGOMIR*
Affiliation:
School of Computer Science and Mathematics, Victoria University, PO Box 14428, Melbourne City, 8001, VIC, Australia (email: [email protected])
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Abstract

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Some inequalities for superadditive functionals defined on convex cones in linear spaces are given, with applications for various mappings associated with the Jensen, Hölder, Minkowski and Schwarz inequalities.

Keywords

superadditive functionalsconvex conesJensen’s inequalityHölder’s inequalityMinkowski’s inequalitySchwarz’ inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals 26D10: Inequalities involving derivatives and differential and integral operators 46C05: Hilbert and pre-Hilbert spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 401 - 411
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Dragomir, S. S., Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces (Nova Science Publishers, New York, 2007).Google Scholar
[2]Dragomir, S. S. and Mond, B., ‘On the superadditivity and monotonicity of Schwarz’s inequality in inner product spaces’, Makedon Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi 15(2) (1994), 5–22.Google Scholar
[3]Dragomir, S. S., Pečarić, J. and Persson, L. E., ‘Properties of some functionals related to Jensen’s inequality’, Acta Math. Hungar. 70 (1996), 129–143.CrossRefGoogle Scholar