The strong convergence of a KM–CQ-like algorithm for a split feasibility problem

Abstract

It is well known that the Krasnosel'skii–Mann algorithm and the CQ algorithm for a split feasibility problem are not strongly convergent. In this paper, we present a KM–CQ-like algorithm with strong convergence, which combines the KM algorithm with the CQ algorithm by introducing two parameter sequences for solving the split feasibility problem. Under some parametric controlling conditions, the strong convergence of the algorithm is shown. Finally, we propose a modified KM–CQ-like algorithm and establish its strong convergence theorem.