Approximating common fixed points of averaged self-mappings with applications to the split feasibility problem and maximal monotone operators in Hilbert spaces

摘要

In this paper, a modified proximal point algorithm for finding common fixed points of averaged self-mappings in Hilbert spaces is introduced and a strong convergence theorem associated with it is proved. As a consequence, we apply it to study the split feasibility problem, the zero point problem of maximal monotone operators, the minimization problem and the equilibrium problem, and to show that the unique minimum norm solution can be obtained through our algorithm for each of the aforementioned problems. Our results generalize and unify many results that occur in the literature. MSC:47H10, 47J25, 68W25.