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Abstract
Let P be an ordered topological space and a multivalued mapping for which
and 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.