• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.93-102
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• 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 $\left\$\mid$ Tx - Ty \right\$\mid$ \leq \left\$\mid$ x - y \right\$\mid$$ 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 $T_i$.