On Smithson’s fixed point theorem for order preserving multifunctions
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. It also contains new results on the structure of the set of fixed points and monotone comparative statics.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Optimization and Variational Analysis
Economic theories and models
Publication details
- Journal / source
- Economics Letters
- Volume
- 263
- Pages
- 112917–112917
- Publication date
- 6 March 2026
- Language
- EN