A Note on Smithson (1971) "Fixed Points of Order Preserving Multifunctions''

2023/03/27 by Kono, Haruki
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.15483

Abstract

Smithson (1971) ``Fixed points of order preserving multifunctions'' gives a fixed point theorem for a self correspondence on a partially ordered set, but its proof has an error. This paper points it out by constructing a counterexample and proves the theorem correctly.

Related

• Order-theoretical fixed point theorems for correspondences and application in game theory
• Order-Preserving Variants of The Basic Principles of Functional Analysis
• Replication via Invalidating the Applicability of the Fixed Point Theorem
• A fixed point theorem for COFEs
• Y is a least fixed point combinator