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

摘要

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