×

zbMATH — the first resource for mathematics

Selections of the best and near-best approximation operators and solarity. (English, Russian) Zbl 1423.41041
Proc. Steklov Inst. Math. 303, 10-17 (2018); translation in Tr. Mat. Inst. Steklova 303, 17-25 (2018).
New significant results are given on the metric projections in the selections of the near-best approximation sets, named suns, in the finite-dimensional Banach spaces.

MSC:
41A50 Best approximation, Chebyshev systems
41A28 Simultaneous approximation
41A35 Approximation by operators (in particular, by integral operators)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alimov, A. R., Monotone path-connectedness of Chebyshev sets in the space C(Q), Sb. Math., 197, 1259-1272, (2006) · Zbl 1147.41011
[2] Alimov, A. R., Preservation of approximative properties of Chebyshev sets and suns in a plane, Moscow Univ. Math. Bull., 63, 198-201, (2008) · Zbl 1304.41018
[3] Alimov, A. R., Local solarity of suns in normed linear spaces, J. Math. Sci., 197, 447-454, (2014) · Zbl 1314.46018
[4] Alimov, A. R., Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces, Izv. Math., 78, 641-655, (2014) · Zbl 1303.41018
[5] Alimov, A. R., Selections of the metric projection operator and strict solarity of sets with continuous metric projection, Sb. Math., 208, 915-928, (2017) · Zbl 1426.41039
[6] Alimov, A. R., Continuity of the metric projection and local solar properties of sets, (2017)
[7] Alimov, A. R., A monotone path-connected set with outer radially lower continuous metric projection is a strict sun, Sib. Math. J., 58, 11-15, (2017) · Zbl 1376.46014
[8] Alimov, A. R.; Shchepin, E. V., Convexity of Chebyshev sets with respect to tangent directions, Russ. Math. Surv., 73, 366-368, (2018) · Zbl 1404.41009
[9] Alimov, A. R.; Tsar’kov, I. G., Connectedness and other geometric properties of suns and Chebyshev sets, J. Math. Sci., 217, 683-730, (2016) · Zbl 1361.46012
[10] Alimov, A. R.; Tsar’kov, I. G., Connectedness and solarity in problems of best and near-best approximation, Russ. Math. Surv., 71, 1-77, (2016) · Zbl 1350.41031
[11] Blatter, J.; Morris, P. D.; Wulbert, D. E., Continuity of the set-valued metric projection, Math. Ann., 178, 12-24, (1968) · Zbl 0189.42904
[12] Bogatyi, S. A., Topological Helly theorem, Fundam. Prikl. Mat., 8, 365-405, (2002) · Zbl 1028.52004
[13] Ş. Cobzaş, Functional Analysis in Asymmetric Normed Spaces (Birkhäuser, Basel, 2013), Front. Math. · Zbl 1266.46001
[14] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings (Springer, Dordrecht, 2006). · Zbl 1107.55001
[15] Kamal, A., On proximinality and sets of operators. I: Best approximation by finite rank operators, J. Approx. Theory, 47, 132-145, (1986) · Zbl 0596.41048
[16] Karimov, U. H.; Repovš, D., On the topological Helly theorem, Topology Appl., 153, 1614-1621, (2006) · Zbl 1094.54016
[17] Konyagin, S. V., On continuous operators of generalized rational approximation, Mat. Zametki, 44, 404, (1988) · Zbl 0694.41022
[18] Shchepin, E. V.; Brodskii, N. B., Selections of filtered multivalued mappings, Proc. Steklov Inst. Math., 212, 209-229, (1996) · Zbl 0873.54022
[19] Tsar’kov, I. G., Continuous ε-selection, Sb. Math., 207, 267-285, (2016) · Zbl 1347.41047
[20] Tsar’kov, I. G., Local and global continuous ε-selection, Izv. Math., 80, 442-461, (2016) · Zbl 1356.46013
[21] I. G. Tsar’kov, “Some applications of geometric theory of approximations,” in Differential Equations. Mathematical Analysis (VINITI, Moscow, 2017), Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 143, pp. 63-80.
[22] Tsar’kov, I. G., Continuous selection from the sets of best and near-best approximation, Dokl. Math., 96, 362-364, (2017) · Zbl 1401.41023
[23] Vlasov, L. P., Approximative properties of sets in normed linear spaces, Russ. Math. Surv., 28, 1-66, (1973) · Zbl 0293.41031
[24] Wegmann, R., Some properties of the peak-set-mapping, J. Approx. Theory, 8, 262-284, (1973) · Zbl 0264.41021
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.