Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1180.47040
Cianciaruso, Filomena; Marino, Giuseppe; Muglia, Luigi; Yao, Yonghong
(Yao, Yong-hong)
On a two-step algorithm for hierarchical fixed point problems and variational inequalities. (English)
[J] J. Inequal. Appl. 2009, Article ID 208692, 13 p. (2009). ISSN 1029-242X/e

The paper is concerned with the variational inequality problem of finding $x^* \in \text{Fix}(T)$ with $\langle (I-S)x^*, x-x^* \rangle \geq 0$ for all $x\in \text{Fix}(T)$, where $T,S: C\to C$ are nonexpansive mappings such that Fix$(T)$, the set of fixed points set of $T$, is nonempty, and $C$ is a closed convex subset of a Hilbert space $H$. Let $f: C \to C$ be a contraction. The authors study convergence properties of the iterative process $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n) T y_n$, $y_n=\beta_n S x_n+(1-\beta_n) x_n$, where $\alpha_n,\beta_n \in [0,1]$.
[Mikhail Yu. Kokurin (Yoshkar-Ola)]

MSC 2000:: *47J20 Inequalities involving nonlinear operators
49J40 Variational methods including variational inequalities
47J25 Methods for solving nonlinear operator equations (general)

Keywords: fixed points; variational inequalities; contractive mappings; iterative methods

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]