On the conditions of existence coincidence points for mapping in partially ordered spaces

A.V. Arutyunov, E.S. Zhukovsky, S.E. Zhukovskii studied the coincidence points for mappings of partially ordered spaces in particular, it was proved that an covering and monotone mapping, acting from a partially ordered space $(X, {\succeq}_{_{_X}})$ to a partially ordered space $(Y, {\succeq}_{_{_Y}})$, have a coincidence point. It is shown that the conditions of this assertion can be weakened: the binary relation ${\succeq}_{_{_Y}} $ should not be in order. We give an appropriate result and and demonstrate an example of mappings satisfying its conditions, but to which the results of the cited work are not applicable