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

  • Tatiana Fomenko
  • Dmitrii PodoprikhinEmail author


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.


Fixed point Coincidence point Partial order Isotone mapping Order homotopy 

Mathematics Subject Classification

54H25 06A06 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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