Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces

Abstract

The split feasibility problem is to find a point x∗ with the property that x∗∈ C and Ax∗∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y, respectively, and A is a bounded linear operator from X to Y. 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 relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposed CQ algorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.