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Quadratic reverses of the triangle inequality for Bochner integral in Hilbert spaces

Published online by Cambridge University Press:  17 April 2009

Sever S. Dragomir
Sever S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University of Technology, PO Box 14428, MCMC Vic. 8001, Australia, e-mail: [email protected]
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Some quadratic reverses of the continuous triangle inequality for the Bochner integral of vector-valued functions in Hilbert spaces are given. Applications of complex-valued functions are provided as well.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 451 - 462
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Diaz, J.B. and Metcalf, F.T., ‘A complementary triangle inequality in Hilbert and Banach spaces’, Proc. Amer. Math. Soc. 17 (1966), 88–97.CrossRefGoogle Scholar
[2]Dragomir, S.S., ‘Reverses of the continuous triangle inequality for Bochner integral of vector valued function in Hilbert spaces’, (preprint), RGMIA Res. Rep. Coll. 7 (2004). Supplement, Article 11. [Online: http://rgmia.vu.edu.au/v7(E).html].Google Scholar
[3]Dragomir, S.S., ‘Additive reverses of continuous triangle inequality for Bochner integral of vector valued functions in Hilbert spaces’, (preprint), RGMIA Res. Rep. Coll. 7 (2004), Supplement, Article 12. [Online: http://rgmia.vu.edu.au/v7(E).html].Google Scholar
[4]Karamata, J., Teorija i Praksa Stieltjesova integrala (Serbo-Croatian), Srpska Akademija Nauka, Posebna Izdanja 144 (Matematički Institut, Kn. 1, Belgrade, 1949).Google Scholar
[5]Marden, M., The geometry of the zeros of a polynomial in a complex variable, Amer. Math. Soc. Math. Surveys 3 (American Mathematical Society, New York, 1949).Google Scholar
[6]Mitrinović, D.S., Pečarić, J.E. and Fink, A.M., Classical and new inequalities in analysis (Kluwer Academic Publishers, Dordrecht, Boston, London, 1993).CrossRefGoogle Scholar
[7]Petrovich, M., ‘Module d'une somme’, L' Ensignement Mathématique 19 (1917), 53–56.Google Scholar
[8]Wilf, H.S., ‘Some applications of the inequality of arithmetic and geometric means to polynomial equations’, Proc. Amer. Math. Soc. 14 (1963), 263–265.CrossRefGoogle Scholar
[9]Yosida, K., Functional analysis, (6th edition) (Springer-Verlag, Berlin, 1980).Google Scholar