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A Unified Iterative Treatment for Solutions of Problems of Split Feasibility and Equilibrium in Hilbert Spaces

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  • Young-Ye Huang
  • Chung-Chien Hong

Abstract

We at first raise the so called split feasibility fixed point problem which covers the problems of split feasibility, convex feasibility, and equilibrium as special cases and then give two types of algorithms for finding solutions of this problem and establish the corresponding strong convergence theorems for the sequences generated by our algorithms. As a consequence, we apply them to study the split feasibility problem, the zero point problem of maximal monotone operators, and the equilibrium problem and to show that the unique minimum norm solutions of these problems can be obtained through our algorithms. Since the variational inequalities, convex differentiable optimization, and Nash equilibria in noncooperative games can be formulated as equilibrium problems, each type of our algorithms can be considered as a generalized methodology for solving the aforementioned problems.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:613928
    DOI: 10.1155/2013/613928
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    References listed on IDEAS

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    1. 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).
    2. Yonghong Yao & Yeong-Cheng Liou & Naseer Shahzad, 2012. "A Strongly Convergent Method for the Split Feasibility Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, October.
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    Cited by:

    1. 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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