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On Preservation of Common Fixed Points and Coincidences Under a Homotopy of Mapping Families of Ordered Sets

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Abstract

In the case of Banach spaces, there are theorems stating the invariance of the fixed point property of mappings under a homotopy. In this paper, we consider this problem in the case of ordered sets. As the main results, we present theorems on the preservation of the property of a family of mappings to have a common fixed point by an order homotopy.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Tatiana Fomenko & Dmitrii Podoprikhin

Authors
  1. Tatiana Fomenko
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  2. Dmitrii Podoprikhin
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Correspondence to Dmitrii Podoprikhin.

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The paper is dedicated to the sixtieth birthday of Professor Aram Vladimirovich Arutyunov.

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Fomenko, T., Podoprikhin, D. On Preservation of Common Fixed Points and Coincidences Under a Homotopy of Mapping Families of Ordered Sets. J Optim Theory Appl 180, 34–47 (2019). https://doi.org/10.1007/s10957-018-1412-4

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  • DOI: https://doi.org/10.1007/s10957-018-1412-4

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