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Strongly unique best approximation in Banach spaces. II. (English) Zbl 0657.41022
The author continues his study of strongly unique best approximation initiated in a previous paper under the same title [J. Approximation Theory 47, 184-194 (1986; Zbl 0615.41027)]. He shows that a best approximation by elements of a sun in a uniformly convex Banach space is strongly unique locally, and gives the global analogies also. He applies the latter results to derive strong uniqueness theorems for Lebesgue, Hardy and Sobolev spaces.
Reviewer: S.Aljančić

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
Zbl 0615.41027
Full Text: DOI
[1] Barros-Neto, J, An introduction to the theory of distributions, (1973), Dekker New York · Zbl 0273.46026
[2] Björnestal, B.O; Björnestal, B.O; Björnestal, B.O, Continuity of the metric projection operator III, the preprint series of the department of mathematics, () · Zbl 0428.41024
[3] Cheney, E.W, Introduction to approximation theory, (1966), McGraw-Hill New York · Zbl 0161.25202
[4] Clarkson, J.A, Uniformly convex spaces, Trans. amer. math. soc., 40, 396-414, (1936) · Zbl 0015.35604
[5] Dunford, N; Schwartz, J, ()
[6] Duren, W.L, Theory of Hp spaces, (1970), Academic Press New York
[7] Efimov, N; Steckin, S, Some properties of chebyshcv sets, Dokl. akad. nauk SSSR, 118, 17-19, (1958)
[8] Figiel, T, An example of infinite dimensional reflexive Banach space non-isomorphic to its Cartesian square, Studia math., 42, 295-306, (1972) · Zbl 0213.12801
[9] Figiel, T, On the moduli of convexity and smoothness, Studia math., 56, 121-151, (1976) · Zbl 0344.46052
[10] Hanner, O, On the convexity of Lp and lp, Ark. mat., 3, 239-244, (1956) · Zbl 0071.32801
[11] Hardy, G.H; Littlewood, J.E; Pólya, G, Inequalities, (1934), Cambridge · Zbl 0010.10703
[12] Klambauer, G, Real analysis, (1973), Elsevier New York · Zbl 0263.28001
[13] Lindenstrauss, J; Tzafriri, L, Classical Banach spaces II. function spaces, (1979), Springer-Verlag Berlin · Zbl 0403.46022
[14] Meir, A, On the uniform convexity of Lp spaces, Illinois J. math., 28, 420-424, (1984) · Zbl 0562.46014
[15] Prus, B; Smarzewski, R, Strongly unique best approximation and centers in uniformly convex spaces, J. math. anal. appl., 121, 10-21, (1987) · Zbl 0617.41046
[16] Schwartz, L, Geometry and probability in Banach spaces, () · Zbl 0555.46007
[17] Smarzewski, R, Strongly unique best approximation in Banach spaces, J. approx. theory, 47, 184-194, (1986) · Zbl 0615.41027
[18] Smarzewski, R, Strongly unique minimization of functionals in Banach spaces with applications to theory of approximation and fixed points, J. math. anal. appl., 115, 155-172, (1986) · Zbl 0593.49004
[19] Smarzewski, R, Classical and extended strong unicity of approximation in Banach spaces, (1986), Mariae Curie-Sklodowska University Lublin, [Polish]
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