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Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

Author

Listed:
  • Kriengsak Wattanawitoon
  • Poom Kumam

Abstract

We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:174796
    DOI: 10.1155/2011/174796
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    Cited by:

    1. Yaqin Wang, 2012. "A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Kamonrat Nammanee & Suthep Suantai & Prasit Cholamjiak, 2012. "Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. 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).

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