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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
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    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. 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.
    3. 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.
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