Abstract
In this paper, we propose a viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general Hilbert spaces. Under some mild conditions, we prove that our algorithms strongly converge to a solution of the split common fixed point problem, which is also the unique solution of the variational inequality problem. Finally, we show the convergence and effectiveness of the algorithms by two numerical examples.
Highlights
(11) is the bounded perturbation resilient and, under some mild conditions, our algorithms strongly converge to a solution of the split common fixed point problem, which is the unique solution of the variational inequality problem (13)
The SCFPP is an inverse problem that consists in finding a point in a fixed point set such that its image under a bounded linear operator belongs to another fixed point set
Many iterative algorithms have been developed to solve these kinds of problems
Summary
Let H1 and H2 be two real Hilbert spaces with the inner product h·, ·i and the induced norm k · k. In 2014, combining the Moudafi method with the Halpern iterative method, Kraikaew and Saejung [8] proposed a new iterative algorithm which does not involve the projection operator to solve the split common fixed point problem. Their algorithm generates a sequence { xn }. Mainly based on the above works [6,20,22], we prove that our main iterative method (11) is the bounded perturbation resilient and, under some mild conditions, our algorithms strongly converge to a solution of the split common fixed point problem, which is the unique solution of the variational inequality problem (13). We give two numerical examples to demonstrate the effectiveness of our iterative schemes
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