Abstract
In this paper, motivated by the idea of the split feasibility problem, we consider the split common null point problem in Banach spaces. Then, using Halpern's type iteration, we prove a strong convergence theorem for finding a solution of the split common null point problem in Banach spaces. The result seems to be the first one to study it outside Hilbert spaces. As application, we get a new strong convergence theorem which is connected with the split common null point problem and an equilibrium problem.