A Viscosity Approximation Method for the Split Feasibility Problems

  • Jitsupa Deepho
  • Poom Kumam


In this paper, we discuss the strong convergence of the viscosity approximation method for solving the split feasibility problem in Hilbert spaces. Consider also the iteration process \( \{ x_{n} \} \), where \( x_{0} \in C \) is arbitrary and \( x_{n + 1} = (1 - \alpha_{n} )P_{C} (I - \xi A^{*} (I - P_{Q} )A)x_{n} + \alpha_{n} f(x_{n} ),n \ge 1 \) where \( \alpha_{n} \in (0,1) \). The main result present in this paper improve and extend some recent result done by Xu [Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 (2010) 105018] and some others.


CQ algorithm Metric projection Split feasibility problem Strong convergence theorem Variational inequality problem Viscosity approximation method 



The first author was supported by the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0033/2554) and the King Mongkut’s University of Technology Thonburi. Moreover, this study was supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology ThonburiBangkokThailand

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