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Approximating Iterations for Nonexpansive and Maximal Monotone Operators

Author

Listed:
  • Zhangsong Yao
  • Sun Young Cho
  • Shin Min Kang
  • Li-Jun Zhu

Abstract

We present two algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive operator in Hilbert spaces. We show that these two algorithms converge strongly to the minimum norm common element of the zero of the sum of two monotone operators and the fixed point of a nonexpansive operator.

Suggested Citation

  • Zhangsong Yao & Sun Young Cho & Shin Min Kang & Li-Jun Zhu, 2015. "Approximating Iterations for Nonexpansive and Maximal Monotone Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:451320
    DOI: 10.1155/2015/451320
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    References listed on IDEAS

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    1. Kriengsak Wattanawitoon & Poom Kumam, 2012. "A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Kriengsak Wattanawitoon & Poom Kumam, 2012. "A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-27, January.
    3. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-39, December.
    4. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Uamporn Witthayarat & Yeol Je Cho & Poom Kumam, 2012. "Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, April.
    6. Kriengsak Wattanawitoon & Poom Kumam, 2011. "Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-31, February.
    7. Uamporn Witthayarat & Yeol Je Cho & Poom Kumam, 2012. "Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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