Summary: Using the idea of Tikhonov’s regularization, we present properties of the approximating curve for the split feasibility problem (SFP) and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, C. Byrne
’s [Inverse Probl. 18, No. 2, 441–453 (2002; Zbl 0996.65048
algorithm (Byrne, 2002) has only weak convergence. We introduce a modification of Byrne’s
algorithm in such a way that strong convergence is guaranteed and the limit is also the minimum-norm solution of SFP.