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Dynamical and proximal approaches for approximating fixed points of quasi-nonexpansive mappings

  • Hadi Khatibzadeh
  • Mohsen Rahimi Piranfar
  • Jamal Rooin
Article
  • 125 Downloads

Abstract

In this paper, we derive some weak and strong convergence results for a nonhomogeneous differential equation with a Lipschitz quasi-nonexpansive mapping. We also consider a discrete version that provides an iterative algorithm for approximating a fixed point of the mapping. We state some weak and strong convergence results related to this algorithm. Finally, we compare this algorithm with the classical algorithms for approximating fixed points of quasi-nonexpansive mappings, and show the advantage of the proposed algorithm via convergence rates.

Keywords

Quasi-nonexpansive mapping fixed point evolution equation asymptotic behavior proximal point algorithm rate of convergence 

Mathematics Subject Classification

Primary 47E05 65J15 Secondary 65J08 65B99 

Notes

Acknowledgements

The authors thank the referee for his/her very careful reading of the manuscript and helpful suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hadi Khatibzadeh
    • 1
  • Mohsen Rahimi Piranfar
    • 2
  • Jamal Rooin
    • 2
  1. 1.Department of MathmaticsUniversity of ZanjanZanjanIran
  2. 2.Department of MathematicsInstitute for Advanced Studies in Basic SciencesZanjanIran

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