Composite algorithms for minimization over the solutions of equilibrium problems and fixed point problems (Q610880)

Summary: The purpose of this paper is to solve the minimization problem of finding \(x^*\) such that \(x^*=\arg \min_{x\in \Gamma }\| x\|^2\), where \(\Gamma \) stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to \(x^*\).