Continuity of the set-valued metric projection. (English) Zbl 0189.42904
Keywords:
functional analysisReferences:
| [1] | Blatter, J.: Zur stetigen Abh?ngigkeit der Menge der besten Approximierenden eines Elementes in einem normierten reellen Vektorraum, to appear in the Proceedings of the Symposium on Numerical Analysis and Approximation Theory held at Oberwolfach, Black Forest, November, 1966. · Zbl 0184.15301 |
| [2] | – Zur Stetigkeit von mengenwertigen metrischen Projektionen. Schriften des Rheinisch-Westf?lischen Instituts f?r Instrumentelle Mathematik an der Universit?t Bonn, Ser. A, Nr. 16 (zugleich Forschungsberichte des Landes Nordrhein-Westfalen, Nr. 1870). |
| [3] | Brown, A. L.: Bestn-dimensional approximation of functions. Proc. London Math. Soc.14, 577-594 (1964). · Zbl 0129.04702 · doi:10.1112/plms/s3-14.4.577 |
| [4] | Buck, R. C.: Applications of duality in approximation theory. Proc. of Symposium on Approximation of Functions, Ed. H. L. Garabedian, pp. 27-43. New York: Elsevier Publishing Co. 1965. · Zbl 0147.11204 |
| [5] | Day, M. M.: Normed linear spaces. Berlin-G?ttingen-Heidelberg: Springer 1958. |
| [6] | Efimov, N. V., and S. B. Stechkin: Approximative compactness and Chebychev sets. Dokl. Akad. Nauk. SSSR140, 522-524 (1961) (Russian), translated in Sov. Math. Dokl.3, 1226-1228 (1962). |
| [7] | Fan, Ky: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sci. USA38, 121-126 (1952). · Zbl 0047.35103 · doi:10.1073/pnas.38.2.121 |
| [8] | Gillman, L., and M. Jerison: Rings of continuous functions. New York: Van Nostrand 1960. · Zbl 0093.30001 |
| [9] | Holmes, R., and B. Kripke: Smoothness of approximation. To appear, see Abstract 636-138, Notices Amer. Math. Soc. |
| [10] | Kelley, J. L.: General topology. New York: Van Nostrand 1955. · Zbl 0066.16604 |
| [11] | Klee, V.: Convexity of Chebychev sets. Math. Ann.142, 292-304 (1961). · Zbl 0091.27701 · doi:10.1007/BF01353420 |
| [12] | – Remarks on nearest points in normed linear spaces. ?Proceedings of the Colloquium on Convexity, Copenhagen 1965?, Copenhagen 1967, 168-176. |
| [13] | Michael, E.: Topologies on spaces of subsets. Trans. Amer. Math. Soc.71, 152-182 (1951). · Zbl 0043.37902 · doi:10.1090/S0002-9947-1951-0042109-4 |
| [14] | Singer, I.: Some remarks on approximative compactness. Rev. Roumaine de Math. Pure et Appl.9, 167-177 (1964). · Zbl 0166.39405 |
| [15] | Tatarkiewicz, K.: Une th?orie g?n?ralis?e de la meilleure approximation. Ann. Univ. Mariae Curie-Sklodowska6, 31-46 (1952). |
| [16] | Vlasov, L. P.: Chebychev sets in Banach spaces. Dokl. Akad. Nauk. SSSR141, 19-20 (1961) (Russian). Translated in Sov. Math. Dokl.3, 1373-1374 (1962). |
| [17] | ?? Approximately convex sets in Banach spaces. Dokl. Akad. Nauk. SSSR163, 18-21 (1965). |
| [18] | Wulbert, D. E.: Continuity of metric projections-approximation theory in a normed linear lattice. Thesis, the University of Texas Computation Center, Austin, 1966. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
