Abstract:
The paper is concerned with properties of sets admitting a continuous selection from the set of nearly best approximations. Necessary and sufficient conditions are put forward for the existence of continuous additive and multiplicative ε-selections on closed sets. Sufficient conditions are given for the existence of continuous selections for stable set-valued mappings with not-necessarily-convex values.
Bibliography: 8 titles.
This publication is cited in the following 21 articles:
I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
I. G. Tsar'kov, “Approximative and structural properties of sets in asymmetric spaces”, Izv. Math., 86:6 (2022), 1240–1253
I. G. Tsar'kov, “Properties of monotone path-connected sets”, Izv. Math., 85:2 (2021), 306–331
T. Erdelyi, “The asymptotic distance between an ultraflat unimodular polynomial and its conjugate reciprocal”, Trans. Am. Math. Soc., 374:5 (2021), 3077–3091
I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
I. G. Tsar’kov, “Some Applications of Geometric Theory of Approximations”, J Math Sci, 245:1 (2020), 64
A. R. Alimov, “Continuity of the metric projection and local solar properties of sets: continuity of the metric projection and solar properties”, Set-Valued Var. Anal., 27:1 (2019), 213–222
I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008
I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
A. R. Alimov, “Bounded contractibility of strict suns in three-dimensional spaces”, J. Math. Sci., 250:3 (2020), 385–390
I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669
I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928
I. G. Tsar'kov, “Continuous selection from the sets of best and near-best approximation”, Dokl. Math., 96:1 (2017), 362–364
A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
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