Generic power convergence of operators in banach spaces
Dan Butnariu, Simeon Reich, Alexander J. Zaslavski · Numerical Functional Analysis and Optimization · 1999
Let K be a closed convex subset of a Banach space X. We consider complete metric spaces of self-mappings of K which are nonexpansive with respect to a convex function on X. We prove that the iterates of a generic operator in these spaces converge strongly. In some cases the limits do not depend on the initial points and are the unique fixed point of the operator.