In this work, we establish two new self-adaptive parallel algorithms to solve the generalized split common fixed point problem which is to find a point which belongs to the intersection of finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. Under suitable assumptions, the weak and strong convergence theorems are analysed. The obtained results generalize and improve the recent results announced by many other authors in the framework of split inverse problem. As a direct consequence of our two main algorithms, we obtain several new algorithms. Preliminary numerical experiments are provided to illustrate the efficiency and implementation of our new methods and also to compare with others.

在这项工作中，我们建立了两种新的自适应并行算法来解决广义分裂公共不动点问题，该问题是找到一个属于有限族的不动点集的demimetric 映射的交集的点，使得它的图像在一个有限的线性变换的数量属于图像空间中另一个有限族的固定点集的二度映射的交集。在适当的假设下，分析了弱收敛定理和强收敛定理。所获得的结果推广和改进了许多其他作者在分裂逆问题框架中公布的最新结果。作为我们两个主要算法的直接结果，我们获得了几个新算法。