Integral equations and inequalities of Volterra type for functions defined in partially ordered spaces

The paper considers Volterra type integral operators acting in L₂(T), where T is a partially ordered topological space as well as equations and inequalities related to them. For the linear operators of this type it is shown that they are quasinilpotent. Explicit estimates for the solutions of linear integral inequalities have been obtained. Nonlinear equations and inequalities have also been considered.