| 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: |
|
| Hits: 3302 |
| Download times: 2276 |
| Abstract: |
| 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 $T$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.01.022 |
| View Full Text View/Add Comment |
