Generating Halpern-type iterative schemes to solve fixed point and null point problems

This study establishes three types of iterative scheme generating methods (ISGMs), each of which yields infinitely many Halpern-type strong convergence theorems. The first result strengthens the previous Mann-type result that guarantees only weak convergence to common fixed points of nonlinear mappings. Next, we exploit resolvents for approximating null points of maximal monotone multi-valued mappings. A mixed-type result is also presented, which simultaneously solves fixed point and null point problems. We explicitly present several variations of iterative schemes derived from the main theorems, including multi-step iterative methods. We also study iterative methods for solving split common null point problems, as applications.