On the Torricellian point in inner product spaces

• Autorzy: Dragomir S. , Comanescu D.
• Języki publikacji: EN

Abstrakty

EN

The concept of Torricellian point related to a set of n vectors in normed linear spaces is introduced and the general properties obtained. The existence and uniqueness of the Torricellian point in inner product spaces are established.

Słowa kluczowe

EN

Torrellian points; normed space; inner product spaces

PL

punkty Torrelliana; przestrzeń unormowana; iloczyn wewnętrzny przestrzeni

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 3
• Strony: 639--650
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Dragomir S.

autor

Comanescu D.

• School of Computer Science and Mathematics, Victoria University, P O Box 14428, MCMC 8001, VIC, Australia,

Bibliografia

• [1] D. Amir, Characterisation of Inner Product Spaces, Birkhauser-Verlag, Basel, 1986.
• [2] M. Baronti, E. Casini and P. L. Papini, Equilateral sets and their central points, Rend. di Mat., Ser VII, 13 (1993), 133-148.
• [3] B. Beauzamy and M. Maurey, Points minimax et ensembles optimeaux dans les espaces de Banach, J. Funct. Anal. 24 (1977), 107-139.
• [4] S. S. Dragomir, D. Comănescu, Y. J. Cho and S. S. Kim, On Torricelli's problem in inner product spaces, Austral. Math. Soc. Gaz. 27 (4) (2000), 173-180.
• [5] A. Daurat, A. Del Longo and M. Nivat, Medians of discrete sets according to a linear distance, Discrete Comput. Geom. 23 (2000), no. 4, 465-483.
• [6] J. Gatial and P. Kapralik, On median point of the system of elements of A-structure, Math. Slovaca 51 (2001), no. 3, 275-280.
• [7] R. B. Holmes, A Course on Optimization and Best Approximation, Lecture Notes, Math. 257, Springer-Verlag, Berlin, 1972.