HYBRID EXTRAGRADIENT METHODS FOR FINDING MINIMUM-NORM SOLUTIONS OF SPLIT FEASIBILITY PROBLEMS

In this paper, we consider the split feasibility problem (SFP) on a nonempty closed convex subset C of a Hilbert space of arbitrary dimension. When C is given as the common fixed point set of nonexpansive mappings, combining Mann's iterative method, Korpelevich's extragradient method and the hybrid steepest-descent method, we develop an iterative algorithm. This algorithm provides the strong convergence to the minimum-norm solution of the SFP. On the other hand, we study the hybrid extragradient methods for finding a common element of the solution set Gamma of the SFP and the set Fix(S) of fixed points of a strictly pseudocontractive mapping S. We propose an iterative algorithm which generates sequences converging weakly to an element of Fix(S) boolean AND Gamma.