HYBRID EXTRAGRADIENT-LIKE APPROXIMATION METHOD WITH REGULARIZATION FOR SOLVING SPLIT FEASIBILITY AND FIXED POINT PROBLEMS

The purpose of this paper is to investigate the problem of finding a common element of the fixed point set Fix(S) of a nonexpansive mapping S and the solution set Gamma of the split feasibility problem (SFP) in real Hilbert spaces. We introduce a hybrid extragradient-like approximation method with regularization, which is based on the well-known extragradient method, a hybrid (or outer approximation) method, and a regularization method. The method produces three sequences which are shown to converge strongly to the same common element of Fix(S) boolean AND Gamma. In addition, we also prove a new weak convergence theorem by a modified extragradient method with regularization for finding an element of Fix(S)boolean AND Gamma. These results represent the supplementation, improvement, extension and development of the corresponding results in the very recent literature.