<p>In this paper, we introduce an efficient method for solving self-adaptive split equilibrium and fixed-point problems in a real Hilbert space. We prove the strong convergence of the recursive sequence generated by the proposed scheme. The method employs a subgradient extragradient technique, leveraging pseudomonotone equilibrium bifunctions, and incorporates a highly accurate procedure for updating the regularization parameters without requiring prior knowledge of the norm of the involved bounded nonlinear operator. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithm. The results confirm the efficiency and practicality of our new scheme. Notably, the integration of regularization parameters and inertial extrapolation steps significantly enhances performance, outperforming commonly used methods in the existing literature.</p>

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Self-adaptive subgradient extragradient algorithm for solving equilibrium and fixed point problems in hilbert spaces

  • Francis O Nwawuru,
  • Jeremiah N. Ezeora,
  • Habib ur Rehman,
  • Jen-Chih Yao

摘要

In this paper, we introduce an efficient method for solving self-adaptive split equilibrium and fixed-point problems in a real Hilbert space. We prove the strong convergence of the recursive sequence generated by the proposed scheme. The method employs a subgradient extragradient technique, leveraging pseudomonotone equilibrium bifunctions, and incorporates a highly accurate procedure for updating the regularization parameters without requiring prior knowledge of the norm of the involved bounded nonlinear operator. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithm. The results confirm the efficiency and practicality of our new scheme. Notably, the integration of regularization parameters and inertial extrapolation steps significantly enhances performance, outperforming commonly used methods in the existing literature.