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Iterative selection methods for common fixed point problems. (English) Zbl 1106.47057
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:
 47J25 Iterative procedures (nonlinear operator equations) 65J15 Equations with nonlinear operators (numerical methods) 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces
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