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Cauchy-schwarz functionals

Published online by Cambridge University Press:  17 April 2009

Y. J. Cho ,
S. S. Dragomir ,
S. S. Kim  and
C. E. M. Pearce
Y. J. Cho
Affiliation:
Department of Mathematics, Gyeongsang National University, Chinju, Korea
S. S. Dragomir
Affiliation:
Department of Mathematics, Dongeui University, Pusan 614–714, Korea
S. S. Kim
Affiliation:
School of Communication and Informatics, Victoria University of Technology, PO Box 14428, Melbourne Vic. 8001, Australia
C. E. M. Pearce
Affiliation:
Applied Mathematics Department, The University of Adelaide, Adelaide SA 5005, Australia
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Abstract

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We treat a class of functionals which satisfy the Cauchy–Schwarz inequality. This appears to be a natural unifying concept and subsumes inter alia isotonic linear functional and sublinear positive isotonic functionals. Striking superadditivity and monotonicity properties are derived.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 479 - 491
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Dragomir, S.S. and Sándor, J., ‘Some inequalities in prehilbertian spaces’,in Proceedings of the National Conference on Geometry and Topology,1987 (Univ. Bucureşti, Bucharestol, 1988), pp. 73–76.Google Scholar
[2]Dragomir, S.S., ‘On an inequality of Tiberiu Popoviciu I’, (Preprint 89–6), in Seminar on functional equations, approximation and convexity (University Babeş-Bolyai, Cluj-Napoca, 1989), pp. 139–145.Google Scholar
[3]Dragomir, S.S., ‘On some operatorial inequalities in Hilbert spaces’, Bul. Ştiinţ. Inst. Politehn. Cluj-Napoca Ser. Mat. Mec. Apl. Construc. MaŞ. 30 (1987), 23–28.Google Scholar
[4]Dragomir, S.S., ‘Inequality of Cauchy–Buniakowski–Schwarz's type for positive linear functionals’, Gaz. Metod. 9 (1988), 162–166.Google Scholar
[5]Dragomir, S.S., ‘Some refinements of Cauchy–Schwarz's inequality’, Gaz. Mat. Metod. 10 (1989), 93–95.Google Scholar
[6]Dragomir, S.S.On Cauchy–Buniakowski–Schwarz inequality for isotonic functional, Seminar on optimization theory 8 (1989), 27–34.Google Scholar
[7]Dragomir, S.S. and Ionescu, N.M., ‘Some refinement of Cauchy–Buniakowski–Schwarz in-equality for sequences’,in Proceedings of the Third Symp. Of Math. and its Appl.(1989) (Rom. Acad., Timişoara, 1990), pp. 79–82.Google Scholar
[8]Dragomir, S.S. and Arslangić, S.Z., ‘An improvement of Cauchy–Buniakowski–Schwarz's inequality’, Mat. Bilten. 16 (1992), 77–80.Google Scholar
[9]Dragomir, S.S., Milošević, D.M. and Arslangić, S.Z., ‘A Cauchy–Buniakowski–Schwarz inequality for Lipschitzian functions’, Zb. Rad. (Kraguejevac) 14 (1993), 25–28.Google Scholar
[10]Mitrinović, D.S., Pečarić, J.E. and Fink, A.M., Classical and new inequalities in analysis (Kluwer, Dordrecht, 1993).CrossRefGoogle Scholar