On fixed points of multifunctions in ordered spaces

Abstract

Let P be an ordered topological space and a multivalued mapping for whichand X 1≤x 2 imply y 1≤y 2 for some y 2∊Fx 2 Several fixed point theorems are derived for F under the above condition and some extra conditions imposed on P and/or F. The use of a generalized iteration method allows us to drop all the continuity properties of F, and even the topology of P from these conditions. Some of the results obtained are new also for single-valued mappings. Applications are given to mapping families and operator equations.