Hybrid method for equilibrium problems and fixed point problems of finite families of nonexpansive semigroups (Q380420)

Let \(C\) be a nonempty closed convex subset of a real Hilbert space \(H\) and \(\phi\) a real bifunction on \(C^2\). Assume that \(\mathcal{F}:=\bigcap^{m}_{i=1}F(\mathcal{T}_i)\cap EP(\phi)\not=\emptyset,\) where \(\mathcal{T}_i:=\{T_i(t)\}_{t\geq 0}\) \((i=1,\dots,m)\) and every \(\{T_i(t)\}_{t\geq 0}\) is a nonexpansive semigroup on \(C\). Under some basic assumptions on \(\phi\), this paper presents two sequences converging strongly to \(P_\mathcal{F}x_0\) for an initial point \(x_0\in C\).