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Preservation of the existence of fixed and coincidence points under homotopy of mappings of ordered sets

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Abstract

In problems of topology and analysis, well-known theorem on the preservation by any continuous homotopy of the property of a mapping to have a fixed point and the property of a pair of mappings to have a coincidence point are extensively applied. Thus, for contraction mappings and some of their generalizations, Frigon’s results on the preservation of the property to have a fixed point by a homotopy of a special type are known. This paper presents theorems on the preservation by order homotopy of the property of a pair of mappings to have a coincidence point. As a corollary, conditions under which such a homotopy preserves the property of a mapping to have a fixed point are obtained.

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Authors and Affiliations

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

    D. A. Podoprikhin & T. N. Fomenko

Authors
  1. D. A. Podoprikhin
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  2. T. N. Fomenko
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Correspondence to T. N. Fomenko.

Additional information

Original Russian Text © D.A. Podoprikhin, T.N. Fomenko, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 4, pp. 402–405.

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Podoprikhin, D.A., Fomenko, T.N. Preservation of the existence of fixed and coincidence points under homotopy of mappings of ordered sets. Dokl. Math. 96, 591–593 (2017). https://doi.org/10.1134/S1064562417060199

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  • DOI: https://doi.org/10.1134/S1064562417060199

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