Nonlinear Ergodic Theorem for Positively Homogeneous Nonexpansive Mappings in Banach Spaces
Wataru Takahashi, Ngai‐Ching Wong, Jen‐Chih Yao · Numerical Functional Analysis and Optimization · 2013
Recently, two retractions (projections), which are different from the metric projection and the sunny nonexpansive retraction in a Banach space, were found. In this article, using nonlinear analytic methods and new retractions, we prove a nonlinear ergodic theorem for positively homogeneous and nonexpansive mappings in a uniformly convex Banach space. The limit points are characterized by using new retractions.