Strong convergence theorems of $k$-strict pseudo-contractions in Hilbert spaces

Title:

Strong convergence theorems of $k$-strict pseudo-contractions in Hilbert spaces

Creator:

Qin, Xiaolong, Kang, Shin Min, and Shang, Meijuan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8279c0f3-d3ff-4559-9c34-906545c23c48
uuid:8279c0f3-d3ff-4559-9c34-906545c23c48

Subject:

Hilbert space, nonexpansive mapping, strict pseudo-contraction, iterative algorithm, and fixed point

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

695-706

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:3

Harvested from:

CDK

Metadata only:

false