Existence and Convergence Theorems for Global Minimization of Best Proximity Points in Hilbert Spaces

  • Raweerote Suparatulatorn
  • Watcharaporn Cholamjiak
  • Suthep SuantaiEmail author


In order to solve global minimization problems involving best proximity points, we introduce general Mann algorithm for nonself nonexpansive mappings and then prove weak and strong convergence of the proposed algorithm under some suitable conditions in real Hilbert spaces. Furthermore, we also provide numerical experiment to illustrate the convergence behavior of our proposed algorithm.


General Mann algorithm Global minimization problem Best proximity point problem Nonexpansive mapping 

Mathematics Subject Classification (2010)

41A29 90C26 47H09 



R. Suparatulatorn and S. Suantai would like to thank the Royal Golden Jubilee (RGJ) Ph.D. Programme (PHD/0021/2559) and Chiang Mai University for the financial support. W. Cholamjiak would like to thank the Thailand Research Fund under the project MRG6080105 and University of Phayao.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of ScienceChiang Mai UniversityChiang MaiThailand
  2. 2.School of ScienceUniversity of PhayaoPhayaoThailand

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