IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/479438.html
   My bibliography  Save this article

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, Hindawi, vol. 2012, pages 1-13, November.
    • Handle: RePEc:hin:jnlaaa:479438
    DOI: 10.1155/2012/479438
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2012/479438.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2012/479438.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/479438?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnlaaa:479438. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.