Parallel iterative methods for solving the generalized split common null point problem in Hilbert spaces

Abstract

We study the recently introduced generalized split common null point problem in Hilbert spaces. In order to solve this problem, we propose two new parallel algorithms and establish strong convergence theorems for both of them. Our schemes combine the hybrid and shrinking projection methods with the proximal point algorithm.

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Acknowledgements

Simeon Reich was partially supported by the Israel Science Foundation (Grant 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 the Vietnam Ministry of Education and Training (B2019-TNA-14). Both authors are grateful to the referees for their detailed reports, useful comments and helpful suggestions.

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Correspondence to Truong Minh Tuyen.

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Reich, S., Tuyen, T.M. Parallel iterative methods for solving the generalized split common null point problem in Hilbert spaces. RACSAM 114, 180 (2020). https://doi.org/10.1007/s13398-020-00901-8

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Keywords

  • Hilbert space
  • Metric projection
  • Monotone operator
  • Nonexpansive mapping
  • Split common null point problem

Mathematics Subject Classification

  • 47H05
  • 47H09
  • 49J53
  • 90C25