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Brosowski, Bruno; Deutsch, Frank

Some new continuity concepts for metric projections. (English) Zbl 0255.41029

Bull. Am. Math. Soc. 78, 974-978 (1972).
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Cited in 2 Reviews
Cited in 10 Documents

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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[1] Dan Amir and Frank Deutsch, Suns, moons, and quasi-polyhedra, J. Approximation Theory 6 (1972), 176 – 201. Collection of articles dedicated to J. L. Walsh on his 75th birthday, VI (Proc. Internat. Conf. Approximation Theory, Related Topics and their Appl., Univ. Maryland, College Park, Md., 1970). · Zbl 0238.41014
[2] Edgar Asplund, Čebyšev sets in Hilbert space, Trans. Amer. Math. Soc. 144 (1969), 235 – 240.
[3] Jörg Blatter, Zur Stetigkeit von mengenwertigen metrischen Projektionen, Forschungsber. Landes Nordrhein-Westfalen Nr. 1870, Westdeutscher Verlag, Cologne, 1967, pp. 17 – 38. · Zbl 0184.15201
[4] J. Blatter, P. D. Morris, and D. E. Wulbert, Continuity of the set-valued metric projection, Math. Ann. 178 (1968), 12 – 24. · Zbl 0189.42904 · doi:10.1007/BF01350621
[5] Jörg Slatter, Weiteste Punkte und nächste Punkte, Rev. Roumaine Math. Pures Appl. 14 (1969), 615 – 621 (German). · Zbl 0205.12301
[6] Bruno Brosowski and Rudolf Wegmann, Charakterisierung bester Approximationen in normierten Vektorräumen, J. Approximation Theory 3 (1970), 369 – 397 (German). · Zbl 0203.12103
[7] Bruno Brosowski and Rudolf Wegmann, On the lower semicontinuity of the set-valued metric projection, J. Approximation Theory 8 (1973), 84 – 100. Collection of articles dedicated to Isaac Jacob Schoenberg on his 70th birthday, I. · Zbl 0288.41016
[8] B. Brosowski, Über eine Fixpunkteigenschaft der metrischen Projektion, Computing (Arch. Elektron. Rechnen) 5 (1970), 295 – 302 (German, with English summary). · Zbl 0209.17801
[9] Bruno Brosowski and Frank Deutsch, On some geometric properties of suns, J. Approximation Theory 10 (1974), 245 – 267. · Zbl 0272.41020
[10] A. L. Brown, Best \?-dimensional approximation to sets of functions, Proc. London Math. Soc. (3) 14 (1964), 577 – 594. · Zbl 0129.04702 · doi:10.1112/plms/s3-14.4.577
[11] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402
[12] H. Hahn, Reelle Funktionen, Akademie Verlagsgesellschaft, Leipzig, 1932; reprint, Chelsea, New York, 1948. · JFM 58.0242.05
[13] Victor Klee, Remarks on nearest points in normed linear spaces, Proc. Colloquium on Convexity (Copenhagen, 1965) Kobenhavns Univ. Mat. Inst., Copenhagen, 1967, pp. 168 – 176.
[14] B. Kripke, Unpublished.
[15] Joram Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. No. 48 (1964), 112. · Zbl 0141.12001
[16] Peter D. Morris, Metric projections onto subspaces of finite codimension, Duke Math. J. 35 (1968), 799 – 808. · Zbl 0167.42301
[17] E. V. Ošman, Continuity of metric projection and some geometric properties of the unit sphere in a Banach space, Dokl. Akad. Nauk SSSR 185 (1969), 34 – 36 (Russian).
[18] Ivan Singer, On set-valued metric projections, Linear operators and approximation (Proc. Conf., Math. Res. Inst., Oberwolfach, 1971) Birkhäuser, Basel, 1972, pp. 217 – 233. Internat. Ser. Numer. Math., Vol. 20.
[19] S. B. Stečkin, Approximation properties of sets in normed linear spaces, Rev. Math. Pures Appl. 8 (1963), 5 – 18 (Russian).
[20] L. P. Vlasov, On almost convex sets in Banach spaces, Dokl. Akad. Nauk SSSR 163 (1965), 18 – 21 (Russian).
[21] L. P. Vlasov, Čebyšev sets and approximately convex sets, Mat. Zametki 2 (1967), 191 – 200 (Russian).
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