Abstract:
The concept of orderly
covers extend to mappings acting from an ordered space $X$ into space $Y$ with a reflexive binary relation. An assertion is obtained about the existence of a solution $x\in X$ of the equation $\Upsilon(x, x) = y,$ where $y\in Y,$ the mapping $\Upsilon:X^2\to Y$ one by one from the arguments is a covering, and on the other — antitone. An example of a concrete
an equation satisfying the assumptions of the proved assertion, to which are not applicable
known results, since $Y$ is not an ordered space.
Keywords:
ordered space, reflexive binary relation, covering mapping, antitone mapping, solvability of the operator equation.
The work is partially supported by the Russian Fund for Basic Research (project № 17-41-680975, № 17-01-00553, № 16-01-00386).
Received: 27.03.2018
Bibliographic databases:
Document Type:
Article
UDC:517.988.63, 512.562
Language: Russian
Citation:
S. Benarab, E. S. Zhukovskiy, “About covering mappings with values in the space with a reflexive binary relation”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018), 210–215
\Bibitem{BenZhu18}
\by S.~Benarab, E.~S.~Zhukovskiy
\paper About covering mappings with values in the space with a reflexive binary relation
\jour Tambov University Reports. Series: Natural and Technical Sciences
\yr 2018
\vol 23
\issue 122
\pages 210--215
\mathnet{http://mi.mathnet.ru/vtamu71}
\crossref{https://doi.org/10.20310/1810-0198-2018-23-122-210-215}
\elib{https://elibrary.ru/item.asp?id=35213528}
Citation in format AMSBIB
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