# Convergence of approximate sequences for compositions of nonexpansive mappings in banach spaces

• Jung, Jong-Soo (Department of Mathematics, Dong-A University, Pusan 604-714) ;
• Kim, Tae-Hwa (Department of Applied Mathematics, Pukyong National University, Pusan 608-737)
• Published : 1997.02.01

#### Abstract

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 $T_i$.

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