IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p747-d1349691.html
   My bibliography  Save this article

Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem

Author

Listed:
  • Ahmed Alamer

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Mohammad Dilshad

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

Abstract

In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems ( S p CNPP ) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples.

Suggested Citation

  • Ahmed Alamer & Mohammad Dilshad, 2024. "Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem," Mathematics, MDPI, vol. 12(5), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:747-:d:1349691
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/747/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/747/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li-Jun Zhu & Yonghong Yao, 2023. "Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    2. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    3. Mohammad Akram & Mohammad Dilshad & Arvind Kumar Rajpoot & Feeroz Babu & Rais Ahmad & Jen-Chih Yao, 2022. "Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    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 & Somyot Plubtieng & Natthaphon Artsawang & Purit Thammasiri, 2023. "Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems," Mathematics, MDPI, vol. 11(13), pages 1-21, June.
    2. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2021. "Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    3. Pawicha Phairatchatniyom & Poom Kumam & Yeol Je Cho & Wachirapong Jirakitpuwapat & Kanokwan Sitthithakerngkiet, 2019. "The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications," Mathematics, MDPI, vol. 7(6), pages 1-22, June.
    4. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.
    5. Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.
    6. Che, Haitao & Li, Meixia, 2016. "The conjugate gradient method for split variational inclusion and constrained convex minimization problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 426-438.
    7. Mohd Asad & Mohammad Dilshad & Doaa Filali & Mohammad Akram, 2023. "A Modified Viscosity-Type Self-Adaptive Iterative Algorithm for Common Solution of Split Problems with Multiple Output Sets in Hilbert Spaces," Mathematics, MDPI, vol. 11(19), pages 1-18, October.

    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:gam:jmathe:v:12:y:2024:i:5:p:747-:d:1349691. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.