Strong convergence theorems for nonexpansive mappings in banach spaces
Jong‐Yeoul Park, Jong-Soo Jung, Jae-Ug Jeong · Communications of the Korean Mathematical Society · 1996
In this paper, we prove for a nonexpansive mapping T that under certain conditions the trajectory $t \to G_t(x), t \in [0,1]$, defined by the equation $G_t(x) = (1 - t)x + tTG_t(x)$ strongly converges to a fixed point of T as $t \to 1^{-1}$.