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An iterative method with residual vectors for solving the fixed point and the split inclusion problems in Banach spaces

  • Prasit Cholamjiak
  • Suthep Suantai
  • Pongsakorn SunthrayuthEmail author
Article
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Abstract

In this paper, we propose an iterative technique with residual vectors for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of a split inclusion problem (SIP) with a way of selecting the stepsizes without prior knowledge of the operator norm in the framework of p-uniformly convex and uniformly smooth Banach spaces. Then strong convergence of the proposed algorithm to a common element of the above two sets is proved. As applications, we apply our result to find the set of common fixed points of a family of mappings which is also a solution of the SIP. We also give a numerical example and demonstrate the efficiency of the proposed algorithm. The results presented in this paper improve and generalize many recent important results in the literature.

Keywords

Resolvent operator Relatively nonexpansive mapping Strong convergence Iterative methods Banach spaces 

Mathematics Subject Classification

47H09 47H10 47J25 47J05 

Notes

Acknowledgements

P. Cholamjiak was supported by the Thailand Research Fund and University of Phayao under Grant RSA6180084. S. Suantai was partially supported by Chiang Mai University.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  • Prasit Cholamjiak
    • 1
  • Suthep Suantai
    • 2
  • Pongsakorn Sunthrayuth
    • 3
    Email author
  1. 1.School of ScienceUniversity of PhayaoPhayaoThailand
  2. 2.Centre of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of ScienceChiang Mai UniversityChiang MaiThailand
  3. 3.Department of Mathematics and Computer Science, Faculty of Science and TechnologyRajamangala University of Technology Thanyaburi (RMUTT)ThanyaburiThailand

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