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Zbl 1106.47057
Hirstoaga, Sever A.
Iterative selection methods for common fixed point problems.
(English)
[J] J. Math. Anal. Appl. 324, No. 2, 1020-1035 (2006). ISSN 0022-247X

The author presents two iterative methods for solving the following problem. Let $(T_n)_{n\in \mathbb{N}}$ and $(S_n)_{n\in \mathbb{N}}$ be two families of quasi-nonexpansive operators from a Hilbert space $H$ to itself such that $\emptyset \neq \bigcap_{n\in \mathbb{N}}\text{Fix}T_n\subset \bigcap_{n\in \mathbb{N}}\text{Fix}S_n$ and $Q:H\rightarrow H$ be a strict contraction. Find (the unique) $\overline{x} \in H$ such that $\overline{x}=P_C(Q\overline{x})$, where $P_C$ is the projection operator on $C$. Finally, applications to monotone inclusions and equilibrium problems are considered.
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
65J15 Equations with nonlinear operators (numerical methods)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: common fixed point; strict contraction; Hilbert space; convergence; iteration; quasi-nonexpansive operator; maximal monotone operator; equilibrium problem

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