In this paper, motivated by the works of Kohsaka and Takahashi (SIAM J Optim 19:824–835, 2008) and Aoyama et al. (J Nonlinear Convex Anal 10:131–147, 2009) on the class of mappings of firmly nonexpansive type, we explore some properties of firmly nonexpansive-like mappings [or mappings of type (P)] in p-uniformly convex and uniformly smooth Banach spaces. We then study the split common fixed point problems for mappings of type (P) and Bregman weak relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an inertial-type shrinking projection algorithm for solving the two-set split common fixed point problems and prove a strong convergence theorem. Also, we apply our result to the split monotone inclusion problems and illustrate the behaviour of our algorithm with several numerical examples s. The implementation of the algorithm does not require a prior knowledge of the operator norm. Our results complement many recent results in the literature in this direction. To the best of our knowledge, it seems to be the first to use the inertial technique to solve the split common fixed point problems outside Hilbert spaces.

本文是受Kohsaka和Takahashi（SIAM J Optim 19：824–835，2008）和Aoyama等人的影响。（J Nonlinear Convex Anal 10：131–147，2009）关于固定非扩张型映射的类别，我们探索了p-一致凸且一致光滑的固定非扩张型映射[或类型（P）的映射]的一些性质Banach空间。然后，我们研究p中的（P）型映射和Bregman弱相对非扩张映射的分裂公共不动点问题-均匀凸和均匀光滑的Banach空间。我们提出了一种惯性型收缩投影算法来解决两类分裂公共不动点问题，并证明了一个强收敛定理。同样，我们将结果应用于分裂单调包含问题，并用几个数值示例s来说明我们算法的行为。该算法的实现不需要操作员规范的先验知识。我们的结果补充了该方向上文献中的许多最新结果。据我们所知，这似乎是第一个使用惯性技术解决希尔伯特空间外的分裂公共不动点问题的方法。