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

Tatiana Fomenko () and Dmitrii Podoprikhin ()
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Tatiana Fomenko: Lomonosov Moscow State University
Dmitrii Podoprikhin: Lomonosov Moscow State University

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 1, No 4, 34-47

Abstract: 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.

Keywords: Fixed point; Coincidence point; Partial order; Isotone mapping; Order homotopy; 54H25; 06A06 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1412-4

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