On Fixed Points of Multifunctions in Ordered Spaces

Abstract

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.

Document Type

Article

DOI

https://doi.org/10.1080/00036819308840206

Keywords

fixed points, multifunctions, Ordered spaces, transfinite sequences

Publication Date

12-1-1993

Journal Title

Applicable Analysis

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