A new proof of Smithson's fixed point theorem for order preserving multifunctions

Haruki Kono and Mark Voorneveld

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Abstract: Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains why Smithson's argument is invalid.

Date: 2023-03, Revised 2026-01
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