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A New Iterative Method for Equilibrium Problems and Fixed Point Problems

Author

Listed:
  • Abdul Latif
  • Mohammad Eslamian

Abstract

Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz‐type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.

Suggested Citation

  • Abdul Latif & Mohammad Eslamian, 2013. "A New Iterative Method for Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:178053
    DOI: 10.1155/2013/178053
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    References listed on IDEAS

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    1. D. R. Sahu & Ngai-Ching Wong & Jen-Chih Yao, 2013. "Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. D. R. Sahu & Ngai-Ching Wong & Jen-Chih Yao, 2013. "Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
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