Skip to main content
SpringerLink
Log in

Continuous selection from the sets of best and near-best approximation

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

The paper studies approximation and structural geometric-topological properties of sets in normed and more general (asymmetric) spaces for which there exists a continuous selection for the best and near-best approximation operators. Sufficient conditions on the metric projection of sets which ensure the existence of a continuous selection for this projection are obtained, and the structural properties of such sets are determined. The existence of a continuous selection for the near-best approximation operator on a finite-dimensional space more general than a normed space is investigated. It is shown that the lower semicontinuity of the metric projection is sufficient for the existence of a continuous selection for the near-best approximation operator in the general case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. R. Alimov and I. G. Tsar’kov, Fund. Prikl. Mat. 63, 21–91 (2014).

    Google Scholar 

  2. A. R. Alimov and I. G. Tsar’kov, Russ. Math. Surveys 71 (1), 1–77 (2016).

    Article  Google Scholar 

  3. S. V. Konyagin, Mat. Zametki 44, 404 (1988).

    MathSciNet  Google Scholar 

  4. E. D. Livshits, Izv.: Math. 67 (1), 91–119 (2003).

    Article  MathSciNet  Google Scholar 

  5. K. S. Ryutin, Math. Notes 73 (1), 142–147 (2003).

    Article  MathSciNet  Google Scholar 

  6. K. S. Ryutin, Math. Notes 71 (2), 236–244 (2002).

    Article  MathSciNet  Google Scholar 

  7. I. G. Tsar’kov, Izv.: Math. 80 (2), 442–461 (2016).

    Article  MathSciNet  Google Scholar 

  8. I. G. Tsar’kov, Sb.: Math. 207 (2), 267–285 (2016).

    MathSciNet  Google Scholar 

  9. I. G. Tsar’kov, Math. Notes 40 (2), 597–610 (1986).

    Article  Google Scholar 

  10. I. G. Tsar’kov, Math. Notes 48 (4), 1052–1058 (1990).

    Article  MathSciNet  Google Scholar 

  11. I. G. Tsar’kov, Math. Notes 89 (4), 572–576 (2011).

    Article  MathSciNet  Google Scholar 

  12. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings (Springer, Dordrecht, 2006).

    MATH  Google Scholar 

  13. E. Michael, J. Ann. Math. Ser. 2 63 (2), 361–381 (1956).

    Article  Google Scholar 

  14. A. R. Alimov, Sb.: Math. 197 (9), 1259–1272 (2006).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    I. G. Tsar’kov

Authors
  1. I. G. Tsar’kov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. G. Tsar’kov.

Additional information

Original Russian Text © I.G. Tsar’kov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 475, No. 4, pp. 373–376.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tsar’kov, I.G. Continuous selection from the sets of best and near-best approximation. Dokl. Math. 96, 362–364 (2017). https://doi.org/10.1134/S1064562417040196

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562417040196

Search

Navigation