Approximating Fixed Points of Pseudocontractive Mapping in Banach Spaces
Received:September 05, 2005  Revised:April 12, 2006
Key Words: pseudocontractive mappings   $p$-uniformly convex Banach spaces   Ishikawa iteration process with errors.
Fund Project:
 Author Name Affiliation YAO Yong-hong Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China CHEN Ru-dong Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Hits: 3179
Let $K$ be a nonempty closed convex subset of a real p-uniformly convex Banach space $E$ and $T$ be a Lipschitz pseudocontractive self-mapping of $K$ with $F(T):=\{x\in K: Tx=x\}\neq \emptyset$. Let a sequence $\{x_n\}$ be generated from $x_1\in K$ by $x_{n+1}=a_nx_n+b_nTy_n+c_nu_n$, $y_n=a'_nx_n+b'_nTx_n+c^{'}_nv_n$ for all integers $n\geq 1$. Then $\|x_n-Tx_n\|\rightarrow 0$ as $n\rightarrow \infty$. Moreover, if $T$ is completely continuous, then $\{x_n\}$ converges strongly to a fixed point of $T$.