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Abstrakty
In this paper, we shall give some properties of superadditivity and mono-tonicity of Gram's determinants in 2-inner product spaces and their applications.
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
807--817
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Department of Mathematics, Dongeui University, Pusan 614-714, Korea
autor
- School of Communications and Informatics, Victoria University of Technology, P.O. Box 14428, Melbourne MC, Victoria 8001, Australia
autor
- Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
Bibliografia
- [1] Y. J. Cho, S. S. Dragomir, S. S. Kim and C. E. M. Pearce, Cauchy-Schwarz functionals, Bull. Austral. Math. Soc., 62 (2000), 479-491.
- [2] Y. J. Cho, M. Matić and J. E. Pečarić, On Gram's determinant in 2-inner product spaces, J. Korean Math. Soc., 38 (2001), 1125-1156.
- [3] Y. J. Cho, C. S. Lin, S. S. Kim and A. Misiak, Theory of2-Inner Product Spaces, Nova Science Publishers, Inc., New York 2001.
- [4] C. Dimininnie, S. Gähler and A. White, 2-inner product spaces, Demonstratio Math., 6 (1973), 525-536.
- [5] C. Dimininie, A. White, 2-inner product spaces and Gäuteaux partial derivatives, Comment. Math. Univ. Carolinae 16 (1975), 115-119.
- [6] S. S. Dragomir, Some new inequalities for Gram determinants in inner product spaces, Univ. Beograd. Publ. Elektrotehn. Fak. ser. Mat. 6 (1995), 38-45.
- [7] S. S. Dragomir, Y. J. Cho and S. S. Kim, Superadditivity and monotonicity of 2-norms generated by inner products and related results, Soochow J. Math. 24 (1)(1998), 13-32.
- [8] S. S. Dragomir, D. Comänescu, Y. J. Cho and S. S. Kim, On Toricelli's problem in inner product spaces, Austral. Math. Soc. Gazette. 27 (2000), 173-180.
- [9] S. S. Dragomir, Y. J. Cho and S. S. Kim, Inequalities of Hadamard's type for Lipschitizian mappings and their applications, J. Math. Anal, and Appl., 245 (2000), 489-501.
- [10] S. Gähler, Lineare 2-normierte Räume, Math. Nachr., 28 (1965), 1-43.
- [11] S. S. Kim, S. S. Dragomir, A. White and Y. J. Cho, On some Grüss type inequality in 2-inner product spaces and applications, PanAmer. J. Math. 11 (2001), 89-97.
- [12] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, Norwell, MA, 1993.
- [13] C. F. Moppert, On the Gram determinant, Quart. J. Math. Oxford, 10 (1959), 161-164.
- [14] J. E. Pečarić, On some classical inequalities in Unitary spaces, Mat. Bilten 16 (1992), 63-72.
- [15] T. Popoviciu, On an inequality, Gaz. Mat. Fiz. A. 11 (64) (1959), 451-461.
- [16] A. White, Y. J. Cho and S. S. Kim, Heron's formula in inner product spaces, Demonstratio Math., 31 (1998), 97-102.
- [17] A. White, Y. J. Cho and S. S. Kim, Characterizations of 2-inner product spaces, Math. Japonica 47 (1998), 239-244.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0008-0005