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Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems

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  • Kamonrat Nammanee
  • Suthep Suantai
  • Prasit Cholamjiak

Abstract

We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.

Suggested Citation

  • Kamonrat Nammanee & Suthep Suantai & Prasit Cholamjiak, 2012. "Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-16, June.
    • Handle: RePEc:hin:jnljam:804538
    DOI: 10.1155/2012/804538
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