On Fixed Points of Multifunctions in Ordered Spaces
Let P be an ordered topological space and F: P → 2P\ø a multivalued mapping for which x1 ≤ y1 Є Fx1 and x1 ≤ x2 imply y1 ≤ y2 for some y2Є Fx2. 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. © 1993, Taylor & Francis Group, LLC. All rights reserved.
fixed points, multifunctions, Ordered spaces, transfinite sequences
Heikkilä, S. "On fixed points of multifunctions in ordered spaces." Applicable Analysis 51, no. 1-4 (1993): 115-127.