2k-inner products in real linear spaces

• Autorzy: Crâşmăreanu M. , Dragomir S. S.
• Języki publikacji: EN

Abstrakty

EN

The notion of 2k-inner product is introduced as a generalization of usual inner product and Q-inner product ([4]-[8]). As a consequence, is denned the notion of 2k-normed space and some properties, e.g. uniformly convexity, Gateaux differentiability and Riesz property of the dual, are given.

Słowa kluczowe

EN

2-inner product; 2k-norm; linear spaces

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 645--656
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Crâşmăreanu M.

• Faculty of Mathematics, University "Al. I. Cuza" of Iaşi, Iaşi 6600, Romania

autor

Dragomir S. S.

• School of Communications and Informatics, Victoria University of Technology, Po Box 14428, MCMC Melbourne, Victoria 8001, Australia

Bibliografia

• [1] D. V. Alekssevsky, S. Marchiafava, Transformations of a quaternionic Kählerian manifold, C. R. Acad. Sci. Paris, Ser. I 320(6) (1995), 703-705.
• [2] D. Amir, Characterizations of Inner Product Spaces, Operator Theory: Advances and Applications 20 (1986), Birkhäuser Verlag.
• [3] Ν. Bourbaki, Topological Vector Spaces-Chapters 1-5, Springer, 1987.
• [4] S. S. Dragomir, Q-normed linear spaces, Proceedings of Romanian Conference on Geometry and Topology, Tirgovişte, April 1986, University of Bucureşti Press, 1988, 69-72.
• [5] S. S. Dragomir, I. Muntean, Linear and continuous functional on complete Q-inner product spaces, Babeş-Bolyai Univ. Sem. Math. Anal. 7 (1987), 59-68.
• [6] S. S. Dragomir, Best approximation in Q-inner-product spaces, Studia Univ. Babeş-Bolyai, Mathematica 34 (1991), 75-80.
• [7] S. S. Dragomir, Representation of continuous linear functionals on complete SQ-inner-product spaces, Analele Universiţări din Timişoara 30 (1992), 241-250.
• [8] S. S. Dragomir, Ν. M. Ionescu, New properties of Q-inner-product spaces, Zb. Rad. (Kragujevac) 14 (1993), 19-24.
• [9] S. S. Dragomir, Smooth normed spaces of (BD)-type, J. Fac. Sci. Univ. Tokyo 39 (1992), 1 - 1 5 .
• [10] A. Misiak, A. Ryż, n-inner product spaces and projections, Mathematica Bohémica 125 (2000), 87-97.
• [11] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Sub-spaces, Publishing House of Romanian Academy & Springer Verlag, 1970.