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Convergence Theorems for Infinite Family of Multivalued Quasi‐Nonexpansive Mappings in Uniformly Convex Banach Spaces

Author

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  • Aunyarat Bunyawat
  • Suthep Suantai

Abstract

We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi‐nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each Ti. Some strong convergence theorems of the proposed method are also obtained for the following cases: all Ti are continuous and one of Ti is hemicompact, and the domain K is compact.

Suggested Citation

  • Aunyarat Bunyawat & Suthep Suantai, 2012. "Convergence Theorems for Infinite Family of Multivalued Quasi‐Nonexpansive Mappings in Uniformly Convex Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:435790
    DOI: 10.1155/2012/435790
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    References listed on IDEAS

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    1. Yicheng Liu & Jun Wu & Zhixiang Li, 2005. "Common fixed points of single-valued and multivalued maps," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-11, January.
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    Cited by:

    1. Fang Zhang & Huan Zhang & Yulong Zhang, 2013. "New Iterative Algorithm for Two Infinite Families of Multivalued Quasi‐Nonexpansive Mappings in Uniformly Convex Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Renu Chugh & Sanjay Kumar, 2014. "Convergence of Infinite Family of Multivalued Quasi‐Nonexpansive Mappings Using Multistep Iterative Processes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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