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A Strongly Convergent Method for the Split Feasibility Problem

Author

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  • Yonghong Yao
  • Yeong-Cheng Liou
  • Naseer Shahzad

Abstract

The purpose of this paper is to introduce and analyze a strongly convergent method which combined regularized method, with extragradient method for solving the split feasibility problem in the setting of infinite‐dimensional Hilbert spaces. Note that the strong convergence point is the minimum norm solution of the split feasibility problem.

Suggested Citation

  • Yonghong Yao & Yeong-Cheng Liou & Naseer Shahzad, 2012. "A Strongly Convergent Method for the Split Feasibility Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:125046
    DOI: 10.1155/2012/125046
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    References listed on IDEAS

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    1. Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong Cheng Liou, 2012. "Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, April.
    2. Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong Cheng Liou, 2012. "Applications of Fixed‐Point and Optimization Methods to the Multiple‐Set Split Feasibility Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Young-Ye Huang & Chung-Chien Hong, 2013. "A Unified Iterative Treatment for Solutions of Problems of Split Feasibility and Equilibrium in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Jinzuo Chen & Mihai Postolache & Li-Jun Zhu, 2019. "Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    3. Ming Ma, 2013. "Algorithmic Approach to the Split Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Chung-Chien Hong & Young-Ye Huang, 2014. "A Strong Convergence Algorithm for the Two‐Operator Split Common Fixed Point Problem in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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