Implicit and explicit algorithms for solving the split feasibility problem

Very recently, Dang and Gao (Inverse Probl 27:015007, 2011) introduced a KM-CQ algorithm with strong convergence for the split feasibility problem. In this paper, we will continue to consider the split feasibility problem. We present two algorithms. First, we introduce an implicit algorithm. Consequently, by discretizing the continuous implicit algorithm, we obtain an explicit algorithm. Under some weaker conditions, we show the strong convergence of presented algorithms to some solution of the split feasibility problem which solves some special variational inequality. As special cases, we obtain two algorithms which converge strongly to the minimum norm solution of the split feasibility problem. Results obtained in this paper include the corresponding results of Dang and Gao (2011) and extend a recent result of Wang and Xu (J Inequalities Appl 2010, doi:10.1155/2010/102085).

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