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<p>In this paper, we propose two Halpern-type forward–backward splitting methods with two-step inertial extrapolation for finding a zero of the sum of two accretive operators in the setting of Banach spaces. Two strong convergence results for the proposed methods are established under different conditions on the inertial parameters. In the first result, strong convergence is proved under certain assumptions imposed on the inertial parameters. In the second result, strong convergence is established without requiring any on-line rule for the inertial parameters or the iterates. Furthermore, we study the strong convergence of another forward–backward splitting method based on a viscosity-type approximation involving a weak contraction. Numerical experiments in compressed sensing and image restoration are provided to demonstrate the advantages and efficiency of the proposed algorithms compared to some existing methods.</p>

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Forward–backward splitting methods with two inertial parameters for solving inclusion problems in Banach spaces

  • 期刊论文

  • 发表日期：

    2026年1月24日

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  • Pongsakorn Sunthrayuth,
  • Ratthaprom Promkam,
  • Kanikar Muangchoo,
  • Woraphak Nithiarayaphaks

摘要

In this paper, we propose two Halpern-type forward–backward splitting methods with two-step inertial extrapolation for finding a zero of the sum of two accretive operators in the setting of Banach spaces. Two strong convergence results for the proposed methods are established under different conditions on the inertial parameters. In the first result, strong convergence is proved under certain assumptions imposed on the inertial parameters. In the second result, strong convergence is established without requiring any on-line rule for the inertial parameters or the iterates. Furthermore, we study the strong convergence of another forward–backward splitting method based on a viscosity-type approximation involving a weak contraction. Numerical experiments in compressed sensing and image restoration are provided to demonstrate the advantages and efficiency of the proposed algorithms compared to some existing methods.