ON ORDER COVERING MAPS IN ORDERED SPACES AND CHAPLYGIN-TYPE INEQUALITIES

The study of covering mappings in partially ordered spaces, started by A. V. Arutyunov, E. S. Zhukovskiy, and S. E. Zhukovskiy (see Topology and its Applications. 2015, v. 179, no. 1) is continued. A set of order covering is defined; this set is investigated for the Nemytskii operator in the space of essentially bounded measurable functions. The equation psi (x, x) = y is treated, where psi is antitonic in the second variable. In terms of the set of order covering for psi in the first variable, a theorem is obtained on the existence of solutions, on their estimates, and on the existence of a lower solution. These results are applied to an implicit integral equation, and certain statements on Chaplygin-type integral inequalities are obtained.