Abstract
In this paper, we introduce a new algorithm for solving the split common fixed point problem (SCFP) for set-valued operators in an infinite dimensional Hilbert spaces. We also present an algorithm for solving split common null point problem of a family of set-valued maximal monotone operators. Considering these algorithms, we establish strong convergence results in an infinite dimensional Hilbert spaces. In support of our results, we further consider the algorithms for a split variational inequality problem and a split optimization problem.