Mean ergodic theorems for nonlinear nonexpansive semigroups in Banach spaces (Nonlinear Analysis and Convex Analysis)
Wataru Takahashi · Institutional Repositories DataBase (IRDB) · 2008
In this article, we deal with weak and strong convergence theorems for abstract semigroups of nonlinear operators in Banach spaces.We first discuss nonlinear mean ergodic theorems for nonexpansive semigroups in a uniformly convex Banach space whose norm is Fr\'echet differentiable.Next, we consider nonlinear ergodic theorems in the case when a Banach space is general and the domains of the nonexpansive semigroups are compact.Further, we deal with weak and strong convergence theorems of Halpem's type and Mann's type for nonexpansive semigroups in Banach spaces.