Weak convergence of a hybrid iterative scheme with errors for equilibrium problems and common fixed point problems (Q2927753)

Let \(C\) be a nonempty closed convex subset of a Hilbert space \(H\). For a bifunction \(\phi:C\times C\rightarrow \mathbb R\), the associated equilibrium problem is to find \(\overline{x} \in C\) such that \(\phi(\overline{x},y)\geq 0 \text{ for all } y \in C\). Denote by \(EP(\phi)\) the set of solutions of the equilibrium problem.NEWLINENEWLINELet also \(T_i:C\rightarrow C\), \(i=1,2,\dots,N\), be a finite family of asymptotically \(k_i\)-strictly pseudocontractive mappings. Denote by \(\mathrm{Fix}\,(T_i)\) the set of fixed points of \(T_i\), i.e., the points \(p\in C\) with \(p=T_i p\).NEWLINENEWLINEIn order to find an element of NEWLINE\[NEWLINE\bigcap_{i=1}^{N} \mathrm{Fix}\,(T_i)\cap EP(\phi)\neq \emptyset,NEWLINE\]NEWLINE the authors consider a hybrid iterative scheme with errors for which a weak convergence theorem (Theorem 2.1) is proven.