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Iterative methods with perturbations for the sum of two accretive operators in q-uniformly smooth Banach spaces

  • Suthep Suantai
  • Prasit Cholamjiak
  • Pongsakorn SunthrayuthEmail author
Original Paper
First Online:
  • 138 Downloads

Abstract

In this work, we introduce implicit and explicit iteration processes with perturbations for solving the fixed point problem of nonexpansive mappings and the quasi-variational inclusion problem. We then prove its strong convergence under some suitable conditions. In the last section of the paper, some applications are given also. The results obtained in this paper extend and improve some known others presented in the literature.

Keywords

Variational inclusion Banach space Strong convergence Iterative method m-Accretive operator 

Mathematics Subject Classification

47H09 47H10 47H17 47J25 49J40 
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Notes

Acknowledgements

S. Suantai would like to thank Chiang Mai University for financial supports, P. Cholamjiak was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248 and P. Sunthrayuth was supported by RMUTT research foundation scholarship of Rajamangala University of Technology Thanyaburi under Grant NRF04066005.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

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

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