| Title:
|
Strong convergence theorems of $k$-strict pseudo-contractions in Hilbert spaces (English) |
| Author:
|
Qin, Xiaolong |
| Author:
|
Kang, Shin Min |
| Author:
|
Shang, Meijuan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
695-706 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K$ be a nonempty closed convex subset of a real Hilbert space $H$ such that $K\pm K\subset K$, $T\: K\rightarrow H$ a $k$-strict pseudo-contraction for some $0\leq k<1$ such that $F(T)=\{x\in K\: x=Tx\}\neq \emptyset $. Consider the following iterative algorithm given by $$ \forall x_1\in K,\quad x_{n+1}=\alpha _n\gamma f(x_n)+\beta _nx_n+((1-\beta _n)I-\alpha _n A)P_KSx_n,\quad n\geq 1, $$ where $S\: K\rightarrow H$ is defined by $Sx=kx+(1-k)Tx$, $P_K$ is the metric projection of $H$ onto $K$, $A$ is a strongly positive linear bounded self-adjoint operator, $f$ is a contraction. It is proved that the sequence $\{x_n\}$ generated by the above iterative algorithm converges strongly to a fixed point of $T$, which solves a variational inequality related to the linear operator $A$. Our results improve and extend the results announced by many others. (English) |
| Keyword:
|
Hilbert space |
| Keyword:
|
nonexpansive mapping |
| Keyword:
|
strict pseudo-contraction |
| Keyword:
|
iterative algorithm |
| Keyword:
|
fixed point |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47J25 |
| idZBL:
|
Zbl 1218.47115 |
| idMR:
|
MR2545650 |
| . |
| Date available:
|
2010-07-20T15:34:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140510 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
