NONLINEAR ERGODIC THEOREMS WITHOUT CONVEXITY FOR NONEXPANSIVE SEMIGROUPS IN HILBERT SPACES

摘要

In this paper, we introduce the concept of common attractive points of a nonexpansive semigroup in a Hilbert space and study fundamental properties for the points. We also prove a nonlinear mean convergence theorem of Baillon's type [3] without convexity for nonexpansiv? semigroups. Using this result, we obtain new and well-known nonlinear mean convergence theorems in a Hilber? space.