EXPLICIT ITERATIVE ALGORITHM FOR SOLVING SPLIT VARIATIONAL INCLUSION AND FIXED POINT PROBLEM FOR THE INFINITE FAMILY OF NONEXPANSIVE OPERATORS

Abstract

In this paper, we introduce a new explicit iterative algorithm for finding a solution of split variational inclusion problem over the common fixed points set of a infinite family of nonexpansive mappings in Hilbert spaces. To reach this goal, the iterative algorithms which combine Tian’s method with some fixed point technically proving methods are utilized for solving the problem. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the considered problem. Our result improves and extends the corresponding results announced by many others.