Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T01:23:22.395Z Has data issue: false hasContentIssue false
  • English
  • Français

QUASILINEARITY OF SOME COMPOSITE FUNCTIONALS WITH APPLICATIONS

Part of: Inequalities

Published online by Cambridge University Press:  17 September 2010

S. S. DRAGOMIR
S. S. DRAGOMIR*
Affiliation:
Mathematics, School of Engineering & 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.

The quasilinearity of certain composite functionals defined on convex cones in linear spaces is investigated. Applications in refining the Jensen, Hölder, Minkowski and Schwarz inequalities are given.

Keywords

additivesuperadditive and subadditive functionalsconvex functionsJensen’s inequalityHölder’s inequalityMinkowski’s inequalitySchwarz’s inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 1 , February 2011 , pp. 108 - 121
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Alzer, H., ‘Sub- and superadditive properties of Euler’s gamma function’, Proc. Amer. Math. Soc. 135(11) (2007), 3641–3648.Google Scholar
[2]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
[3]Dragomir, S. S., ‘Inequalities for superadditive functionals with applications’, Bull. Aust. Math. Soc. 77 (2008), 401–411.Google Scholar
[4]Dragomir, S. S. and Mond, B., ‘On the superadditivity and monotonicity of Schwarz’s inequality in inner product spaces’, Contributions, Macedonian Acad. Sci. Arts 15(2) (1994), 5–22.Google Scholar
[5]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.Google Scholar
[6]Losonczi, L., ‘Sub- and superadditive integral means’, J. Math. Anal. Appl. 307(2) (2005), 444–454.Google Scholar
[7]Trimble, S. Y., Wells, J. and Wright, F. T., ‘Superadditive functions and a statistical application’, SIAM J. Math. Anal. 20(5) (1989), 1255–1259.Google Scholar
[8]Vitolo, A. and Zannier, U., ‘Inequalities for superadditive functions related to a property R [of] convex sets’, Boll. Unione Mat. Ital. A (7) 4(3) (1990), 309–314.Google Scholar
[9]Volkmann, P., ‘Sur les fonctions simultanément suradditives et surmultiplicatives’, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 28(76)(2) (1984), 181–184.Google Scholar