Asymptotic Behavior of Nonexpansive Mappings and Some Geometric Properties in Banach Spaces
Tomoyuki FUJIHIRA · Tokyo Journal of Mathematics · 1984
COROLLARY 2. (i) In Theorem 1, if $X$ is reflexive and strictly con- vex, then $w-\lim_{n\rightarrow\infty}T^{n}x/n=w-\lim_{n\rightarrow\infty}x_{n+1}/a_{n}=-v$ for all $x,$ $x_{0}\in C$ , where $\Vert v\Vert=\inf_{yeC}\Vert Ty-y\Vert$ . (ii) In Theorem 1, if $X^{*}$ has Fr\'echet differentiable norm, then