Generalizations of the Tarski Type Fixed Point Theorems

Abstract

In the present article, by applying our new 2023 Metatheorem and the Brøndsted-Jachymski Principle, we recall and improve fixed point theorems related to Alfred Tarski (1901-1983). First, we obtain various forms of generalizations of the Knaster-Tarski fixed point theorem. Actually, their nature is that, for a chain P with an upper bound v ∈ P in a partially ordered set (X, ≼), a progressive map f : P → P (that is, x ≼ f (x) for all x ∈ P) has a maximal fixed element v ∈ P. Further, we obtain several improved versions of the Tarski-Kantorovitch type fixed point theorems.