IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n259470.html

Convergence Theorems for Common Fixed Points of a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces

Author

Listed:
  • Yuanheng Wang
  • Weifeng Xuan

Abstract

We establish some strong convergence theorems for a common fixed point of a finite family of relatively nonexpansive mappings by using a new hybrid iterative method in mathematical programming and the generalized projection method in a Banach space. Our results improve and extend the corresponding results by many others.

Suggested Citation

  • Yuanheng Wang & Weifeng Xuan, 2013. "Convergence Theorems for Common Fixed Points of a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:259470
    DOI: 10.1155/2013/259470
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/259470
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/259470?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
    ---><---

    References listed on IDEAS

    as
    1. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou, 2012. "Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, December.
    2. Yuanheng Wang, 2012. "Strong Convergence Theorems for Asymptotically Weak -Pseudo- -Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, November.
    3. Wei Xu & Yuanheng Wang, 2012. "Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, October.
    4. Chakkrid Klin-eam & Suthep Suantai & Wataru Takahashi, 2009. "Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    5. Chakkrid Klin-eam & Suthep Suantai & Wataru Takahashi, 2009. "Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-18, November.
    6. Wei Xu & Yuanheng Wang, 2012. "Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou, 2012. "Strong Convergence of a Modified Extragradient Method to the Minimum‐Norm Solution of Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Yuanheng Wang & Huimin Shi, 2014. "A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non‐Self‐Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Yuanheng Wang, 2014. "Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuanheng Wang, 2012. "Strong Convergence Theorems for Asymptotically Weak G‐Pseudo‐Ψ‐Contractive Non‐Self‐Mappings with the Generalized Projection in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Shunhou Fan & Yonghong Yao, 2012. "Strong Convergence of a Projected Gradient Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Kriengsak Wattanawitoon & Poom Kumam, 2012. "A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Muhammad Aslam Noor & Saira Zainab & Yonghong Yao, 2012. "Implicit Methods for Equilibrium Problems on Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Chaichana Jaiboon & Poom Kumam, 2012. "Viscosity Approximation Method for System of Variational Inclusions Problems and Fixed‐Point Problems of a Countable Family of Nonexpansive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Jong Soo Jung, 2012. "Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Xionghua Wu & Yeong-Cheng Liou & Zhitao Wu & Pei-Xia Yang, 2012. "Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. Youli Yu & Pei-Xia Yang & Khalida Inayat Noor, 2012. "Projection Algorithms for Variational Inclusions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    10. Yuanheng Wang & Chunjie Wang, 2013. "Convergence of a New Modified Ishikawa Type Iteration for Common Fixed Points of Total Asymptotically Strict Pseudocontractive Semigroups," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Yaqin Zheng & Jinwei Shi, 2012. "New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Pongsakorn Sunthrayuth & Poom Kumam, 2013. "A New Computational Technique for Common Solutions between Systems of Generalized Mixed Equilibrium and Fixed Point Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    13. Wei Xu & Yuanheng Wang, 2013. "A General Iterative Algorithm with Strongly Positive Operators for Strict Pseudo‐Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    14. Peixia Yang & Yonghong Yao & Yeong-Cheng Liou & Rudong Chen, 2012. "Hybrid Algorithms of Nonexpansive Semigroups for Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    15. Rattanaporn Wangkeeree & Uthai Kamraksa & Rabian Wangkeeree, 2011. "A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    16. Yeong-Cheng Liou & Yonghong Yao & Chun-Wei Tseng & Hui-To Lin & Pei-Xia Yang, 2012. "Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    17. Rabian Wangkeeree & Pakkapon Preechasilp, 2012. "New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi‐Monotone Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    18. Yonghong Yao & Yeong-Cheng Liou, 2010. "Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    19. Siwaporn Saewan & Poom Kumam, 2010. "A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi‐Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).

    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:wly:jnlaaa:v:2013:y:2013:i:1:n:259470. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.