Asymptotic stability in the Schauder fixed point theorem
Volume 131 / 1998
Studia Mathematica 131 (1998), 143-148
DOI: 10.4064/sm-131-2-143-148
Abstract
This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.
