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Mat. Zametki, 2018, Volume 104, Issue 5, Pages 745–754 (Mi mz11821)  

New Criteria for the Existence of a Continuous $\varepsilon$-Selection

I. G. Tsar'kov

Lomonosov Moscow State University

Abstract: We study sets admitting a continuous selection of near-best approximations and characterize those sets in Banach spaces for which there exists a continuous $\varepsilon$-selection for each $\varepsilon>0$. The characterization is given in terms of $P$-cell-likeness and similar properties. In particular, we show that a closed uniqueness set in a uniformly convex space admits a continuous $\varepsilon$-selection for each $\varepsilon>0$ if and only if it is $\mathring{B}$-approximately trivial. We also obtain a fixed point theorem.

Keywords: continuous $\varepsilon$-selection, fixed point.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00295-a
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00295-a.


DOI: https://doi.org/10.4213/mzm11821

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English version:
Mathematical Notes, 2018, 104:5, 727–734

Bibliographic databases:

UDC: 517.982.256
Received: 07.10.2017
Revised: 06.02.2018

Citation: I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Mat. Zametki, 104:5 (2018), 745–754; Math. Notes, 104:5 (2018), 727–734

Citation in format AMSBIB
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