A Note on the Split Common Fixed Point Problem and its Variant Forms

Abstract

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 its variant forms, 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 quasinonexpansive 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 quasinonexpansive mappings.Finally, as a special case of the split feasibility and fixed point equality problems, 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.Results proved in this chapter continue to hold for different type of problems, such as; convex feasibility problem, split feasibility problem and multipleset split feasibility problems.