An extragradient method for solving split feasibility and fixed point problems
The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set ? ? of the split feasibility problem and the set Fix ( S ) of fixed points of a nonexpansive mapping S S in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N.Nadezhkina, W.Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191201], we propose an iterative algorithm for finding an element of Fix ( S ) ? ? . We prove that the sequences generated by the proposed algorithm converge weakly to an element of Fix ( S ) ? ? under mild conditions.
extragradient method fixed point problems regularization split feasibility problems averaged mappings maximal monotone mappings