An inertial method for solving split common fixed point problems

Abstract

In this paper, we introduce a new algorithm which combines the Mann iteration and the inertial method for solving split common fixed point problems. The weak convergence of the algorithm is established under standard assumptions imposed on cost operators. As a consequence, we obtain weak convergence theorems for split variational inequality problems for inverse strongly monotone operators, and split common null point problems for maximal monotone operators. Finally, for supporting the convergence of the proposed algorithms we also consider several preliminary numerical experiments on a test problem.

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Acknowledgements

The authors are grateful to the anonymous referee for valuable suggestions which helped to improve the manuscript. The first author was partially supported by Vietnam Institute for Advanced Study in Mathematics (VIASM). The second author was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project 101.01-2017.315.

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Correspondence to Duong Viet Thong.

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Thong, D.V., Van Hieu, D. An inertial method for solving split common fixed point problems. J. Fixed Point Theory Appl. 19, 3029–3051 (2017). https://doi.org/10.1007/s11784-017-0464-7

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Mathematics Subject Classification

  • 47H10
  • 47J25
  • 47H45
  • 65J15

Keywords

  • Split common fixed point problem
  • split feasibility problem
  • split variational inequality problem
  • split null point problem