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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 1, Pages 168–191 (Mi izv8768)  
Fixed points and coincidences of families of mappings between ordered sets and some metrical consequences

T. N. Fomenko

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We present theorems on common fixed points and coincidences for families of multi-valued mappings of ordered sets. This generalizes some recent results of the author and Podoprikhin as well as the classical theorems of Knaster–Tarski, Smithson and Zermelo. We also consider connections with the Caristi fixed-point theorem and other metrical results.

Keywords: ordered set, multi-valued mapping, fixed point, coincidence point.

DOI: https://doi.org/10.4213/im8768

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English version:
Izvestiya: Mathematics, 2019, 83:1, 151–172

Bibliographic databases:

UDC: 512.562+515.126.83+515.126.4
MSC: 54H25, 55M20, 54F05, 06A06
Received: 02.02.2018

Citation: T. N. Fomenko, “Fixed points and coincidences of families of mappings between ordered sets and some metrical consequences”, Izv. RAN. Ser. Mat., 83:1 (2019), 168–191; Izv. Math., 83:1 (2019), 151–172

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