IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n232765.html

Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces

Author

Listed:
  • Kasamsuk Ungchittrakool

Abstract

The aim of this paper is to provide some existence theorems of a strict pseudocontraction by the way of a hybrid shrinking projection method, involving some necessary and sufficient conditions. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudocontraction in the framework of real Hilbert spaces. In addition, we also provide certain applications of the main theorems to confirm the existence of the zeros of an inverse strongly monotone operator along with its convergent results.

Suggested Citation

  • Kasamsuk Ungchittrakool, 2013. "Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:232765
    DOI: 10.1155/2013/232765
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/232765
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/232765?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. Heinz H. Bauschke & Patrick L. Combettes, 2001. "A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 248-264, May.
    2. Kasamsuk Ungchittrakool, 2012. "An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and 𠜙 -Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, September.
    3. Kasamsuk Ungchittrakool, 2012. "An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and ϕ‐Quasi‐Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Kasamsuk Ungchittrakool, 2011. "Strong Convergence by a Hybrid Algorithm for Finding a Common Fixed Point of Lipschitz Pseudocontraction and Strict Pseudocontraction in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    5. 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.
    6. Kasamsuk Ungchittrakool, 2010. "A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    7. Kasamsuk Ungchittrakool, 2011. "Strong Convergence by a Hybrid Algorithm for Finding a Common Fixed Point of Lipschitz Pseudocontraction and Strict Pseudocontraction in Hilbert Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, August.
    8. 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.
    9. Rabian Wangkeeree & Rattanaporn Wangkeeree, 2009. "The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    10. Rabian Wangkeeree & Rattanaporn Wangkeeree, 2009. "The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-26, November.
    11. Kasamsuk Ungchittrakool, 2010. "A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-17, December.
    Full references (including those not matched with items on IDEAS)

    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. Kasamsuk Ungchittrakool & Duangkamon Kumtaeng, 2013. "An Iterative Shrinking Metric f‐Projection Method for Finding a Common Fixed Point of a Closed and Quasi‐Strictf‐Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Prasit Cholamjiak & Suthep Suantai & Yeol Je Cho, 2012. "Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. 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).
    4. Utith Inprasit & Weerayuth Nilsrakoo, 2011. "A Halpern‐Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    5. 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).
    6. Yaqin Wang, 2012. "A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. 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).
    8. Somyot Plubtieng & Wanna Sriprad, 2009. "Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    9. Pongrus Phuangphoo & Poom Kumam, 2013. "A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi‐ϕ‐Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    10. 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).
    11. Mathew O. Aibinu & Surendra C. Thakur & Sibusiso Moyo, 2020. "Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    12. H. Zegeye & N. Shahzad, 2012. "Convergence Theorems for a Common Point of Solutions of Equilibrium and Fixed Point of Relatively Nonexpansive Multivalued Mapping Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    13. Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed‐Point Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    14. Yanlai Song & Omar Bazighifan, 2022. "Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    15. Yanlai Song & Omar Bazighifan, 2022. "Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    16. Cholamjiak, Watcharaporn & Dutta, Hemen, 2022. "Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    17. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    18. Jing Zhao & Hang Zhang, 2014. "Solving Split Common Fixed‐Point Problem of Firmly Quasi‐Nonexpansive Mappings without Prior Knowledge of Operators Norms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    19. Yasunori Kimura & Kazuhide Nakajo, 2013. "The Problem of Image Recovery by the Metric Projections in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    20. Ali Abkar & Elahe Shahrosvand & Azizollah Azizi, 2017. "The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 5(1), pages 1-18, February.

    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:jnljam:v:2013:y:2013:i:1:n:232765. 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/4185 .

    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.