The authors consider the following multiple-sets split feasibility problem: Find a vector
where is a given -matrix, , are non-empty closed convex sets in , and , are non-empty closed convex sets in .
A new method for solving this problem is proposed, which uses variable step-sizes unlike to other methods known from the literature, whcih use a fixed step-size. The m ethod is an extension and application of the method published by B. S. He, H. Yang, Q. Meng and D. R. Han [J. Optimization Theory Appl. 112, No. 1, 129–143 (2002; Zbl 0998.65066)] to problems with weaker conditions.