Abstract
The paper investigates the relations between the extension properties of bounded bilinear functionals and the approximation properties in 2-normed spaces.
Authors
Costica Mustata
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
Bilinear functionals; 2-normed spaces; best approximation.
Paper coordinates
C. Mustăţa, Şt. Cobzaş, Extension of bilinear functionals and best approximation in 2-normed space, Studia Univ. ”Babeş-Bolyai”, Seria Mathematica, XLIII, Nr.2 (1998), 1-13.
About this paper
Journal
Studia Universitatis “Babes-Bolyai”, Mathematica
Publisher Name
DOI
Print ISSN
1843-3855
Online ISSN
google scholar link
[1] S. Cobzas, C. Mustata, Norm-preserving extension of convex Lipschitz functions, Journal of Approx. Theory 24 (1978), 236-244.
[2] S. Cobzas, C. Mustata, Extension of bilinear operators and best approximaiton in 2-normed spaces, Rev. anal. Numer. Theor. Approx. 25 (1996), 61-75.
[3] C. Diminnie, S. Gahler, A . White, Stgrictly convex linear 2- normed spaces, Math. Nachr. 59(1974), 319-324.
[4] C. Diminnie, S. Gahler, A. White, Remarks on strictly convex and strictly 2-convex 2-normed spaces, Math. Nachr. 88(1979), 363-372.
[5] C. Diminnie, A. White, Some geometric remarks concerning strictly 2-convex 2-normed spaces, Math. Seminar Notes. Kobe Univ., 6(1978(, 245-253.
[6] N. Dunfod, J.T. Schwartz, Linear operators, Part.I: General Theory, Interscience Publishers, New York, 1958.
[7] I. Franic, an extension theorem for bounded linear 2-funcitonals and applications, Math. Japonica, 40(1944), 79-85.
[8] R.W. Freese, Y.J. Cho, Characterization of linear 2-normed spaces, Math. Japonica 40(1944), 115-122.
[9] S. Gahler, 2-Metrische Raume und ihre Topologische Struktur, Math. Nachr. 26(1963/64), 115-148.
[10] S. Gahler, Lineare 2-Normierte Raume, Math. Nachr. 28 (1965), 335-347.
[11] S. Gahler, Uber 2-Banach-Raume, Math. Nachr. 42(1969), 335-347.
[12] K.S. Ha, Y.J. Cho, A. White, Strictly convex and strictly 2-convex 2-normed spaces, Math.Japonica 33(1988), 375-384.
[13] K. Iseki, Mathematics on 2-normed spaces, Bull. Korean Math. Soc. 13 (1976), 127-136.
[14] G. Kothe, Topologische Lineare Raume, vol.I, Springer Verlag, Berlin-Gottingen-Heidelberg, 1960.
[15] S.N.Lal, M. Das, 2-functionals and some extension theorems in linear spaces, Indian J. Pure Appl. Math. 13(8) (1982), 912-919.
[16] S. Mabizela, A characterization of strictly convex linear 2-normed spaces, Questiones Mathematicae 12 (1989), 201-204.
[17] S. Mabizela, On bounded linear 2-funcitonals, Math. Japonica 35 (1990), 51-55.
[18] C. Mustata, Best approximation and unique extension of Lipschitz functions, J.Approx.Theory 19 (1977), 222-230.
[19] R.R. Phelps, Uniqueness of Hahn-Banach extension and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238-255.
[20] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Publishing House of the Romanian Academy and Springer Verlag, Bucharest-Berlin, 1970.
[21] A.G. White, Jr., 2-Banach spaces, Math. Nachr. 42(1969), 43-60.
[22] A.G. White Jr., Yeol Je Cho, Linear mappings on linear 2-normed spaces, Bull. Korean Math. Soc. 21 (1984), 1-6.