Iterative methods for solving the split common fixed point problem of demicontractive mappings in Hilbert spaces

The split common fixed point problem was proposed in recent years which required to find a common fixed point of a family of mappings in one space whose image under a linear transformation is a common fixed point of another family of mappings in the image space. In this paper, we study two iterative algorithms for solving this split common fixed point problem for the class of demicontractive mappings in Hilbert spaces. Under mild assumptions on the parameters, we prove the convergence of both iterative algorithms. As a consequence, we obtain new convergence theorems for solving the split common fixed point problem for the class of directed mappings. We compare the performance of the proposed iterative algorithms with the existing iterative algorithms and conclude from the numerical experiments that our iterative algorithms converge faster than these existing iterative algorithms in terms of iteration numbers.