A Note on the Split Common Fixed Point Problem and its Variant Forms
Adem Kılıçman, L. B. Mohammed · 2018
The split common fixed-point problems has found its applications in various branches of mathematics both pure and applied. It provides us a unified structure to study a large number of nonlinear mappings. Our interest here is to apply these mappings and propose some iterative methods for solving the split common fixed-point problems, and we prove the convergence results of these algorithms. As a special case of the split common fixed problems, we consider the split common fixed-point equality problems for the class of finite family of quasi-nonexpansive mappings. Furthermore, we consider another problem namely split feasibility and fixed-point equality problems and suggest some new iterative methods and prove their convergence results for the class of quasi-nonexpansive mappings. Finally, we consider the split feasibility and fixed-point problems and propose Ishikawa-type extra-gradients algorithms for solving these split feasibility and fixed-point problems for the class of quasi-nonexpansive mappings in Hilbert spaces. In the end, we prove the convergence results of the proposed algorithms.