TITLE: Banach and Knaster-Tarski fixed point theorems -- are they related?
QUESTION [16 upvotes]: It there any known way of obtaining the Banach fixed-point theorem from the Tarski fixed-point theorem or vice-versa?

REPLY [4 votes]: As suggested by Jacques, I turn my comment into an answer.
This is not exactly what you ask for, but it is related. Efe Ok in Section 3.4 in Chapter 6 of his yet-to-be-written book on ordered sets gives a proof of the Banach fixed point theorem using the Kantorovitch-Tarski fixed point theorem: files.nyu.edu/eo1/public/Book-PDF/CHAPTER%205.pdf https://sites.google.com/a/nyu.edu/efeok/books/CHAPTER%205.pdf