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.
 
             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                         
                                                            