Inertial relaxed<i>CQ</i>algorithms for solving a split feasibility problem in Hilbert spaces

Abstract

The split feasibility problem is to find a pointx*with the property thatx*is an element of CandAx*is an element of Q, whereCandQare nonempty closed convex subsets of real Hilbert spacesXandY, respectively, andAis a bounded linear operator fromXtoY. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxedCQalgorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposedCQalgorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.