Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

  • Pham Thanh Hieu
  • Nguyen Thi Thu Thuy
  • Jean Jacques StrodiotEmail author


The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.


Variational inequality Common fixed point Nonexpansive semigroup Accretive mapping Explicit method 

Mathematics Subject Classification

41A65 47H17 47H20 



The authors are very grateful to the referees for their useful comments, which helped to improve the paper.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Faculty of Basic ScienceUniversity of Agriculture and Forestry, Thai Nguyen UniversityQuyet Thang Commune, Thai Nguyen CityVietnam
  2. 2.Department of Mathematics and InformaticsUniversity of Science, Thai Nguyen UniversityThai Nguyen CityVietnam
  3. 3.Department of MathematicsUniversity of NamurNamurBelgium

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