Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 804538, 16 pages.

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

Kamonrat Nammanee, Suthep Suantai, and Prasit Cholamjiak

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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.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 804538, 16 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180254

Digital Object Identifier
doi:10.1155/2012/804538

Mathematical Reviews number (MathSciNet)
MR2948083

Zentralblatt MATH identifier
1323.47074

Citation

Nammanee, Kamonrat; Suantai, Suthep; Cholamjiak, Prasit. Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems. J. Appl. Math. 2012, Special Issue (2012), Article ID 804538, 16 pages. doi:10.1155/2012/804538. https://projecteuclid.org/euclid.jam/1357180254


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