In this paper, we first consider the split common null point problem in two Banach spaces. Then, using the Bregman generalized resolvents of maximal monotone operators, we prove strong convergence theorems of Halpern type iteration for finding a solution of the split common null point problem in two Banach spaces. As an application of our result, we study the split equilibrium problem in general Banach spaces and approximate a solution of the problem for the first time. Our new technique is based on basic properties of a Bregman distance induced by a Bregman function without using Bregman projection or the requirement of Mosco convergence of the sequences produced by the method. It is well known that the Bregman distance does not satisfy either the symmetry property or the triangle inequality which are required for standard distances. So, the results of the paper improve and extend many recent results in the literature.

在本文中，我们首先考虑两个 Banach 空间中的分裂公共零点问题。然后，利用最大单调算子的Bregman广义解算子，我们证明了Halpern型迭代的强收敛定理，用于在两个Banach空间中寻找分裂公共零点问题的解。作为我们结果的应用，我们研究了一般巴拿赫空间中的分裂平衡问题，并首次逼近了该问题的解。我们的新技术基于由 Bregman 函数引起的 Bregman 距离的基本特性，而不使用 Bregman 投影或该方法产生的序列的 Mosco 收敛要求。众所周知，Bregman 距离不满足标准距离所需的对称性或三角不等式。所以，