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Covering Mappings Acting into Normed Spaces and Coincidence Points

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Abstract

We study the solvability of an equation generated by a mapping acting from a metric space into a normed space. For the radii of balls lying in the image of the mapping, we obtain an estimate in terms of covering mappings. Applying this result, we find conditions for the existence of coincidence points of two mappings.

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References

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Funding

This work was supported by a grant of the President of the Russian Federation (project no. MD-2658.2021.1.1). Theorem 1 was obtained by the first author under the support of the Russian Science Foundation (grant no. 20-11-20131).

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Authors and Affiliations

  1. V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997, Russia

    A. V. Arutyunov & S. E. Zhukovskiy

  2. Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051, Russia

    A. V. Arutyunov

Authors
  1. A. V. Arutyunov
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  2. S. E. Zhukovskiy
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Corresponding author

Correspondence to A. V. Arutyunov.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 315, pp. 19–25 https://doi.org/10.4213/tm4233.

Translated by I. Nikitin

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Arutyunov, A.V., Zhukovskiy, S.E. Covering Mappings Acting into Normed Spaces and Coincidence Points. Proc. Steklov Inst. Math. 315, 13–18 (2021). https://doi.org/10.1134/S0081543821050023

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  • DOI: https://doi.org/10.1134/S0081543821050023

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