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Mathematical Notes

, Volume 104, Issue 5–6, pp 727–734 | Cite as

New Criteria for the Existence of a Continuous ε-Selection

  • I. G. Tsar’kovEmail author
Article
  • 12 Downloads

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 ε-selection for each ε > 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 ε-selection for each ε > 0 if and only if it is B-approximately trivial. We also obtain a fixed point theorem.

Keywords

continuous ε-selection fixed point 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.LomonosovMoscow State UniversityMoscowRussia

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