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<p>By combining the inertial technique with hybrid projection algorithm, we introduce a new hybrid projection algorithm with two different inertial terms to solve fixed point problem for a nonexpansive mapping and variational inequality problem for a monotone Lipschitz continuous mapping. A new lemma tool is proposed and proved in this paper, it is very useful and will be used to help to complete the theoretical proof of main conclusions. By utilizing this new lemma tool, the strong convergence of the proposed algorithms are presented. Two numerical experiments are given to illustrate the computational performance of the proposed algorithms at end. </p>

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Convergence theorems of hybrid projection algorithms with two inertial terms for solving fixed point problem

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • S. Q. Weng,
  • G. L. Yu

摘要

By combining the inertial technique with hybrid projection algorithm, we introduce a new hybrid projection algorithm with two different inertial terms to solve fixed point problem for a nonexpansive mapping and variational inequality problem for a monotone Lipschitz continuous mapping. A new lemma tool is proposed and proved in this paper, it is very useful and will be used to help to complete the theoretical proof of main conclusions. By utilizing this new lemma tool, the strong convergence of the proposed algorithms are presented. Two numerical experiments are given to illustrate the computational performance of the proposed algorithms at end.