Maximale Fixpunkte von Intervallfunktionen (Q791283)

A fixed point theorem for interval functions and some modifications are stated. By the theorem, under the only premises of Schauder's fixed point theorem there is a fixed point which is maximal with respect to the inclusion relation. If in addition the interval function is inclusion isotonic, such fixed points can be obtained in a constructive manner. Then the well known fixed point theorems for isotonic, antitonic and sums of such functions in partially ordered Banach spaces are special cases. Applications to linear and nonlinear algebraic equations and to nonlinear integral equations with numerical examples are given.