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A modified contraction-type method for solving monotone inclusion problem in Hilbert spaces

Author

Listed:
  • Wang, Linan
  • Cai, Gang
  • Salisu, Sani
  • Shehu, Yekini

Abstract

We suggest a contraction-type method with a modified self-adaptive step size to solve the monotone inclusion problem in real Hilbert spaces. The sequences generated by our algorithm are convergent strongly under some suitable conditions. We also conduct some numerical experiments to show the effectiveness of our proposed algorithms.

Suggested Citation

  • Wang, Linan & Cai, Gang & Salisu, Sani & Shehu, Yekini, 2026. "A modified contraction-type method for solving monotone inclusion problem in Hilbert spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 749-768.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:749-768
    DOI: 10.1016/j.matcom.2025.07.041
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    References listed on IDEAS

    as
    1. Yonghong Yao & Abubakar Adamu & Yekini Shehu, 2024. "Forward–Reflected–Backward Splitting Algorithms with Momentum: Weak, Linear and Strong Convergence Results," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1364-1397, June.
    2. Lateef O. Jolaoso & Yekini Shehu & Jen-Chih Yao, 2024. "Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 555-584, February.
    3. Paul-Emile Maingé & André Weng-Law, 2024. "Accelerated forward–backward algorithms for structured monotone inclusions," Computational Optimization and Applications, Springer, vol. 88(1), pages 167-215, May.
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