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<p>In this paper, we first introduce an improved inertial projection and contraction method to approximate a common solution of quasimonotone variational inequalities and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varrho\)</EquationSource> </InlineEquation>-demicontractive fixed point problems in real Hilbert spaces. Then the strong convergence result of our method is established. Moreover, by adopting a predetermined exogenous inertial parameter, our algorithm improves the computational efficiency of some strongly convergent inertial algorithms that require the on-line rule to update inertial parameters. Finally, two numerical experiments are shown to demonstrate the effectiveness of our method.</p>

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An improved strongly convergent algorithm for quasimonotone variational inequalities and fixed point problems

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Xingfang Wang,
  • Xia Zhang

摘要

In this paper, we first introduce an improved inertial projection and contraction method to approximate a common solution of quasimonotone variational inequalities and \(\varrho\) -demicontractive fixed point problems in real Hilbert spaces. Then the strong convergence result of our method is established. Moreover, by adopting a predetermined exogenous inertial parameter, our algorithm improves the computational efficiency of some strongly convergent inertial algorithms that require the on-line rule to update inertial parameters. Finally, two numerical experiments are shown to demonstrate the effectiveness of our method.