  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 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, 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 multiple-set
split feasibility problems.
