ALGORITHMS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS APPROACH TO MINIMIZATION PROBLEMS
Yonghong Yao, Y. C. Liou, M. M. Wong · Taiwanese Journal of Mathematics · 2010
In this paper, we introduce two algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Furthermore, we prove that the proposed algorithms converge strongly to a solution of the minimization problem of finding $x^* \in \Gamma$ such that $\left\| x^* \right\| = \min_{x \in \Gamma} \|x\|$ where $\Gamma$ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping.