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<p>In this article, we introduce an inertial self-adaptive algorithm with two different inertial factors for approximating a minimum-norm solution of the split feasibility problems in the framework of Banach spaces. The first of inertial factor is assumed to be a nonnegative bounded sequence in an appropriate interval and in the second one is assumed to be a negative bounded sequence in an appropriate interval. Our proposed algorithm employs a new type of step size selection without any priori knowledge of the operator norm. Under suitable conditions, the strong convergence of the proposed algorithm are established. Finally, we provide several numerical experiments to show the numerical behaviors of the proposed algorithm and compare them with previously algorithms in the literature.</p>

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Inertial self-adaptive algorithm with two different inertial factors for solving split feasibility problems in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年3月19日

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  • Pongsakorn Sunthrayuth,
  • Kanikar Muangchoo,
  • Prasit Cholamjiak,
  • Woraphak Nithiarayaphaks

摘要

In this article, we introduce an inertial self-adaptive algorithm with two different inertial factors for approximating a minimum-norm solution of the split feasibility problems in the framework of Banach spaces. The first of inertial factor is assumed to be a nonnegative bounded sequence in an appropriate interval and in the second one is assumed to be a negative bounded sequence in an appropriate interval. Our proposed algorithm employs a new type of step size selection without any priori knowledge of the operator norm. Under suitable conditions, the strong convergence of the proposed algorithm are established. Finally, we provide several numerical experiments to show the numerical behaviors of the proposed algorithm and compare them with previously algorithms in the literature.