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<p>The paper introduces two new methods, termed relaxed dual inertial extragradient methods, which incorporate a self-adaptive step size strategy. These methods are developed to approximate solutions to pseudomonotone variational inequality problems and fixed-point problems associated with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1187_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\chi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>χ</mi> </math></EquationSource> </InlineEquation>-demicontractive mappings in real Hilbert spaces. The proposed methods offer multiple key advantages. First, both methods utilize variable step sizes that are updated at each iteration based on previous iterates. One major advantage is that these methods do not require prior knowledge of Lipschitz constants or any line-search procedures. Second, by employing a dual inertial scheme, the methods enhance convergence through a step size update rule that adapts iteratively using information from earlier iterations. The strong convergence of the methods is proven under mild assumptions. Additionally, several numerical experiments are conducted to illustrate the performance of the methods and to compare them with existing approaches.</p>

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Strong convergence of dual inertial fixed point algorithms for computing fixed points over the solution set of a variational inequality problem in real hilbert spaces

  • 期刊论文

  • 发表日期：

    2025年2月18日

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  • Kanokwan Sitthithakerngkiet,
  • Habib ur Rehman,
  • Ioannis K. Argyros,
  • Thidaporn Seangwattana

摘要

The paper introduces two new methods, termed relaxed dual inertial extragradient methods, which incorporate a self-adaptive step size strategy. These methods are developed to approximate solutions to pseudomonotone variational inequality problems and fixed-point problems associated with \(\chi \) χ -demicontractive mappings in real Hilbert spaces. The proposed methods offer multiple key advantages. First, both methods utilize variable step sizes that are updated at each iteration based on previous iterates. One major advantage is that these methods do not require prior knowledge of Lipschitz constants or any line-search procedures. Second, by employing a dual inertial scheme, the methods enhance convergence through a step size update rule that adapts iteratively using information from earlier iterations. The strong convergence of the methods is proven under mild assumptions. Additionally, several numerical experiments are conducted to illustrate the performance of the methods and to compare them with existing approaches.