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Zbl 1153.54024
Yao, Yonghong; Liou, Yeong-Cheng; Yao, Jen-Chih
Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.
(English)
[J] Fixed Point Theory Appl. 2007, Article ID 64363, 12 p. (2007). ISSN 1687-1812/e

Let $C$ be a nonempty closed convex subset of a Hilbert space $H$ and $h: C\times C\to\bbfR$ be an equilibrium bifunction, that is, $h(u,u)= 0$ for every $u\in C$. Then one can define the equilibrium problem that is to find an element $u\in C$ such that $h(u,v)\ge 0$ for all $v\in C$.\par In the present paper the authors introduce a new iterative scheme for finding (by strong convergence) a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of nonexpansive mappings in a Hilbert space.
[Jarosław Górnicki (Rzeszów)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
47H09 Mappings defined by "shrinking" properties
47J25 Methods for solving nonlinear operator equations (general)

Keywords: nonexpansive mapping; equilibrium problem; fixed point

Cited in: Zbl 1204.41028 Zbl 1186.47068

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