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Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

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  • Zhou Yinying
  • Cao Jiantao
  • Wang Yali

Abstract

We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).

Suggested Citation

  • Zhou Yinying & Cao Jiantao & Wang Yali, 2014. "Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, April.
    • Handle: RePEc:hin:jnljam:232541
    DOI: 10.1155/2014/232541
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