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New Criteria for the Existence of a Continuous ε-Selection

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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.

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Authors and Affiliations

  1. LomonosovMoscow State University, Moscow, 119991, Russia

    I. G. Tsar’kov

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  1. I. G. Tsar’kov
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Correspondence to I. G. Tsar’kov.

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Original Russian Text © I. G. Tsar’kov, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 5, pp. 745–754.

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Tsar’kov, I.G. New Criteria for the Existence of a Continuous ε-Selection. Math Notes 104, 727–734 (2018). https://doi.org/10.1134/S0001434618110147

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