Hybrid iterative method for split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings

Abstract

In this paper, we propose a hybrid iterative method to approximate a common solution of split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. We prove that sequences generated by the proposed hybrid iterative method converge strongly to a common solution of these problems. Further, we discuss some applications of the main result. We also discuss a numerical example to demonstrate the applicability of the iterative method. The method and results presented in this paper extend and unify the corresponding known results in this area.

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Acknowledgements

The authors are grateful to the anonymous referees for their constructive and helpful comments and suggestions towards the improvement of the original manuscript.

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Correspondence to K. R. Kazmi.

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Kazmi, K.R., Ali, R. & Furkan, M. Hybrid iterative method for split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings. Numer Algor 79, 499–527 (2018). https://doi.org/10.1007/s11075-017-0448-0

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Keywords

  • Split monotone variational inclusion problem
  • Hierarchical fixed point problem
  • Hybrid iterative method
  • Maximal monotone operators
  • Nonexpansive mapping
  • Strong convergence

Mathematics Subject Classifications (2010)

  • 47H09
  • 47J25
  • 49J40
  • 90C99