Iterative selection methods for common fixed point problems (Q852819)

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.