Integral equations and inequalities of Volterra type for functions defined in partially ordered spaces with values in Banach spaces. (English) Zbl 0912.45012

Summary: Linear integral operators of Volterra type acting in \(L_2 (T,B)\) where \(T\) is a partially ordered connected topological space and \(B\) is a Banach space as well as the corresponding equations and inequalities, are considered. It is shown that these operators are quasinilpotent and some explicit estimates for the solutions of the corresponding integral equations and inequalities are obtained.


45N05 Abstract integral equations, integral equations in abstract spaces
45D05 Volterra integral equations
45P05 Integral operators
26D10 Inequalities involving derivatives and differential and integral operators
47G10 Integral operators
47B60 Linear operators on ordered spaces