Weak and strong convergence adaptive algorithms for generalized split common fixed point problems

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.

Automated summary

Two new self-adaptive parallel algorithms are established in this work to solve the generalized split common fixed point problem. Weak and strong convergence theorems are analyzed under suitable assumptions, generalizing and improving recent results by other authors. Several new algorithms are obtained as a direct consequence of the main algorithms, with preliminary numerical experiments provided to illustrate efficiency and implementation.