Choices of variable steps of the CQ algorithm for the split feasibility problem

We consider the CQ algorithm, with choice of steps introduced by Yang (J. Math. Anal. Appl. 302 (2005), 166-179), for solving the split feasibility problem (SFP): Find x Ie{cyrillic, ukrainian} C such that Ax Ie{cyrillic, ukrainian} Q, where C and Q are nonempty closed convex subsets of ℝⁿ and ℝ^m, respectively, and A is an m × n matrix. We convert the SFP to an equivalent convexly constrained nonlinear system of finding a zero in C of an inverse strongly monotone operator, which enables us to introduce new convergent iterative algorithms. Two restrictive conditions of Yang (i.e., the boundedness of Q and the full column rank of A) are completely removed in our new algorithms.