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Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces

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  • Lai-Jiu Lin
  • Zenn-Tsun Yu
  • Chih-Sheng Chuang

Abstract

In this paper, we prove both weak and strong convergence theorems for finding a common element of the solution set for a generalized equilibrium problem, the fixed point set of an asymptotically k-strict pseudo-contraction mapping in the intermediate sense, and the solution set of the variational inequality for a monotone and Lipschitz-continuous mapping by using a new hybrid extragradient method. Our results generalize and improve related results in the literatures. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Lai-Jiu Lin & Zenn-Tsun Yu & Chih-Sheng Chuang, 2013. "Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces," Journal of Global Optimization, Springer, vol. 56(1), pages 165-183, May.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:1:p:165-183
    DOI: 10.1007/s10898-012-9968-2
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    References listed on IDEAS

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    1. O. Chadli & N.C. Wong & J.C. Yao, 2003. "Equilibrium Problems with Applications to Eigenvalue Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 245-266, May.
    2. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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