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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.
MSC:
45N05Abstract integral equations, integral equations in abstract spaces
45D05Volterra integral equations
45P05Integral operators
26D10Inequalities involving derivatives, differential and integral operators
47G10Integral operators
47B60Operators on ordered spaces