An iteration process for nonexpansive mappings with applications to fixed point theory in product spaces
W. A. Kirk · Proceedings of the American Mathematical Society · 1989
A uniform transfinite iteration procedure for selecting fixed points of nonexpansive mappings is introduced. This procedure, which applies to arbitrary nonexpansive mappings in Banach spaces having Kadec-Klee norm and to strictly contractive mappings in reflexive Banach spaces, is used to generalize a fixed point theorem of Kirk and Sternfeld for nonexpansive mappings in product spaces.