STRONG CONVERGENCE THEOREMS BY HYBRID METHODS FOR SOLVING SPLIT COMMON FIXED POINT PROBLEMS IN HILBERT SPACES AND APPLICATIONS

In this paper, using the hybrid method defined by Nakajo and Takahashi and the shrinking projection method defined by Takahashi, Yakeuchi and Kubota, we prove two strong convergence theorems for solving the split common fixed point problem with finding a zero point of a maximal monotone mapping in Hilbert s paces. In two theorems, we use general nonlinear mappings, that is, inverse strongly monotone mappings and general hybrid mapping in Hilbert spaces. by two hybrid methods for the problems. As applications, we get new strong convergence theorems which are connected with the split fixed point problem and the equilibrium problem.