Parallel Iterative Methods for Solving the Split Common Fixed Point Problem in Hilbert Spaces

Abstract

We introduce three new parallel algorithms for solving the split common fixed point problem in Hilbert spaces. Those iterative methods for solving split common fixed point problems which involve step sizes that depend on the norm of a given bounded linear operator are often not easy to implement because one has to compute the norm of this operator. Therefore, in addition to two such algorithms, we also propose a new iterative method involving step sizes which are selected in such a way that the implementation of the method does not require the computation or estimation of the norm of the given operator. Several corollaries of our main results regarding the solution of multiple-set split feasibility, split common null point, split variational inequality and split mixed equilibrium problems are also presented.

Keywords:

• Metric projection
• nonexpansive mapping
• parallel algorithm
• split common fixed point problem

2010 Mathematics Subject Classification:

• 47H05
• 47H09
• 49J53
• 90C25

Acknowledgments

All the authors are grateful to the three referees and to the editor for their many useful comments and helpful suggestions.

Additional information

Funding

The first author was partially supported by the Israel Science Foundation (Grant No. 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. The second author was supported by the Science and Technology Fund of Thai Nguyen University of Sciences.