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.
Fulltext:
PDF file (126 kB)