Abstract:
In asymmetric seminormed and semimetric spaces, sets admitting a continuous ε-selection for any ε>0 are studied. A characterization of closed subsets of a complete symmetrizable asymmetric seminormed space admitting a continuous ε-selection for all ε>0 is obtained. Sufficient conditions for the existence of continuous selections in seminormed linear spaces and semimetric semilinear spaces are put forward. Applications to generalized rational functions in the asymmetric space of continuous functions and in the semilinear space Lh of all boundedly compact convex sets with Hausdorff metric are found. A metric-topological fixed point theorem for a stable set-valued mapping in the space Lh is obtained.
Bibliography: 17 titles.
This publication is cited in the following 16 articles:
I. G. Tsarkov, “Svoistva diskretnogo ne bolee chem schetnogo ob'edineniya mnozhestv v nesimmetrichnykh prostranstvakh”, Matem. sb., 216:2 (2025), 128–144
I.G. Tsar'kov, “Convexity of $\delta$-Suns and $\gamma$-Suns in Asymmetric Spaces”, Russ. J. Math. Phys., 31:2 (2024), 325
I.G. Tsarkov, “Relations Between Various Types of Suns in Asymmetric Spaces”, Russ. J. Math. Phys., 31:3 (2024), 562
I. G. Tsar'kov, “Connectedness in asymmetric spaces”, Journal of Mathematical Analysis and Applications, 527:1 (2023), 127381
A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Russian Math. Surveys, 78:3 (2023), 399–442
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, “Reflexivity for spaces with extended norm”, Russ. J. Math. Phys., 30:3 (2023), 399
I. G. Tsar'kov, “Continuity of a Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 111:4 (2022), 616–623
I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469
A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces $C(q)$ and $L^p$”, Russ. J. Math. Phys., 29:3 (2022), 291–305
I. G. Tsarkov, “Uniformly and locally convex asymmetric spaces”, Russ. J. Math. Phys., 29:1 (2022), 141–148
I. G. Tsar'kov, “Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 112:6 (2022), 1017–1024
I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Math. Notes, 110:5 (2021), 773–783
I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
G. Poonguzali, M. Marudai, Ch. Park, “Multivalued fixed point in Banach algebra using continuous selection and its application to differential inclusion”, J. Appl. Anal. Comput., 8:6 (2018), 1747–1757
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