THE GENERAL ITERATIVE METHODS FOR SPLIT VARIATIONAL INCLUSION PROBLEM AND FIXED POINT PROBLEM IN HILBERT SPACES

摘要

In this paper, we consider and analyze a general iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping, which is the unique solution for the variational inequality in real Hilbert spaces. Furthermore, under reasonable conditions, the sequence generated by the proposed iterative scheme converges strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping, which is a solution of a certain optimization problem related to a strongly positive linear operator. The results presented in this paper improve and extend the corresponding results reported by some authors recently.