On estimates for solutions of systems of convex inequalities

The distance from a given point to the solution set of a system of strict and nonstrict inequalities described by convex functions is estimated. As consequences, estimates for the distance from a given point to the Lebesgue set of a convex function are obtained and sufficient conditions for convex-valued set-valued mappings to be covering are established. © 2015, Pleiades Publishing, Ltd.