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Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications

Author

Listed:
  • Jingling Zhang
  • Yongfu Su
  • Qingqing Cheng

Abstract

The purpose of this paper is to present the notion of weak relatively nonexpansive multi‐valued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces. The weak relatively nonexpansive multivalued mappings are more generalized than relatively nonexpansive multivalued mappings. In this paper, an example will be given which is a weak relatively nonexpansive multivalued mapping but not a relatively nonexpansive multivalued mapping. In order to get the strong convergence theorems for weak relatively nonexpansive multivalued mappings, a new monotone hybrid iteration algorithm with generalized (metric) projection is presented and is used to approximate the fixed point of weak relatively nonexpansive multivalued mappings. In this paper, the notion of multivalued resolvent of maximal monotone operator has been also presented which is a weak relatively nonexpansive multivalued mapping and can be used to find the zero point of maximal monotone operator.

Suggested Citation

  • Jingling Zhang & Yongfu Su & Qingqing Cheng, 2012. "Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:479438
    DOI: 10.1155/2012/479438
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    References listed on IDEAS

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    1. Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
    2. Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2004(3), pages 239-249.
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    Cited by:

    1. Li Wei & Yibin Xin & Ruilan Zhang & Ravi P. Agarwal, 2020. "Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments," Mathematics, MDPI, vol. 8(4), pages 1-21, April.

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