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<p>The main purpose of this paper is to introduce a modified Mann-type algorithm with a new step-length rule for approximating the solution of the monotone inclusion problem and the fixed point problem. Weak convergence is obtained without the prior knowledge of the Lipschitz constant of the mapping. Furthermore, we present several numerical experiments to show the effectiveness of the proposed algorithm.</p>

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A new modified Mann-type method for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces

  • 期刊论文

  • 发表日期：

    2025年6月21日

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  • Shenghua Huang,
  • Gang Cai,
  • Qiao-Li Dong

摘要

The main purpose of this paper is to introduce a modified Mann-type algorithm with a new step-length rule for approximating the solution of the monotone inclusion problem and the fixed point problem. Weak convergence is obtained without the prior knowledge of the Lipschitz constant of the mapping. Furthermore, we present several numerical experiments to show the effectiveness of the proposed algorithm.