Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T02:55:11.916Z Has data issue: false hasContentIssue false
  • English
  • Français

Reverses of the Schwarz inequality generalising a Klamkin–McLenaghan result

Published online by Cambridge University Press:  17 April 2009

Sever S. Dragomir
Sever S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University, PO Box 14428, Melbourne City, VIC 8001, Australia, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

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.

New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 69 - 78
Copyright
Copyright © Australian Mathematical Society 2006

References

Referenes

[1]Dragomir, S.S., ‘Reverse of Schwarz, triangle and Bessel inequalities in inner product spaces’, JIPAM J. Inequal. Pure Appl. Math. 5 (2004), Art. 76. Online: http://jipam.vu.edu.au/article.php?sid=432.Google Scholar
[2]Dragomir, S.S., ‘New reverses of Schwarz, triangle and Bessel inequalities in inner product spaces’, Aust. J. Math. Anal. Appl. 1 (2004), Art. 1. Online: http://ajmaa.org/cgi-bin/paper.pl?string=nrstbiips.tex.Google Scholar
[3]Dragomir, S.S., Advances in inequalities of the Schwarz, Grüss and Bessel type in inner product spaces (Nova Science Publishers Inc., New York, 2005).Google Scholar
[4]Dragomir, S.S., ‘Reverses of the Cauchy-Bunyakovsky-Schwarz inequality for n-tuples of complex numbers’, Bull. Austral. Math. Soc. 69 (2004), 465–480.CrossRefGoogle Scholar
[5]Elezović, N., Marangunić, L. and Pečarić, J., ‘Unified treatment of complemented Schwarz and Gruss inequalities in inner product spaces’, Math. Ineqal. Appl. 8 (2005), 223–232.Google Scholar
[6]Greub, W. and Rheinboldt, W., ‘On a generalisation of an inequality of L.V. Kantorovich’, Proc. Amer. Math. Soc. 10 (1959), 407–415.CrossRefGoogle Scholar
[7]Klamkin, M.S. and McLenaghan, K.G., ‘An ellipse inequality,’, Math. Mag. 50 (1977), 261–263.CrossRefGoogle Scholar
[8]Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis 1 (Springer-Verlag, Berlin, 1925).Google Scholar
[9]Shisha, O. and Mond, B., ‘Bounds on differences of means’, in Inequalities I (Academic Press, New York-London, 1967), pp. 293–308.Google Scholar
[10]Watson, G.S., ‘Serial correlation in regression analysis I’, Biometrika 42 (1955), 327–342.CrossRefGoogle Scholar