Iterative methods for solving the split common fixed point problem of demicontractive mappings in Hilbert spaces
Authors
Chunxiang Zong
 Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China
Yuchao Tang
 Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China
Abstract
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.
Keywords
 Split common fixed point problem
 demicontractive mappings
 cyclic iteration method
 simultaneous iteration method
MSC
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