Convergence of approximate sequences for compositions of nonexpansive mappings in banach spaces
Jong-Soo Jung, Tae-Hwa Kim · Bulletin of the Korean Mathematical Society · 1997
Let C be a nonempty closed convex subset of a Banach space E and let $T_1, \cdots, T_N$ be nonexpansive mappings from C into itself (recall that a mapping $T : C \longrightarrow C$ is nonexpansive if $\left Tx - Ty \right \leq \left x - y \right\$ for all $x, y \in C$). We consider the fixed point problem for nonexpansive mappings : find a common fixed point, i.e., find a point in $\cap_{i=1}^N Fix(T_i)$, where $Fix(T_i) := {x \in C : x = T_i x}$ denotes the set of fixed points of $T_i$.