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<p>The application of a Bregman subgradient extragradient algorithm to pseudomonotone equilibrium and fixed points problems associated with quasi-Bregman nonexpansive mappings is considered. We incorporate a Bregman distance framework and an inertial extrapolation technique to approximate a common solution to both the equilibrium problem and the fixed points of quasi-Bregman nonexpansive mappings within a reflexive Banach space. In addition, we introduce a regulating parameter, denoted by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>, to regulate and enhance the step size of the algorithm such that the cost operator does not rely on the Lipschitz constant. We verify the accuracy and effectiveness of our approach with two numerical examples. We note that the incorporation of our parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation> improves the convergence rate compared to other algorithms. Also, we observed that the smaller the value of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>, the faster the convergence. These results demonstrate the effectiveness of our algorithm and provide contributions that advance existing knowledge in this research domain.</p>

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A novel framework for solving pseudomonotone equilibrium and fixed point problems using bregman techniques

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Basirat Olawunmi Lawal-Akinmade,
  • Kazeem Olalekan Aremu,
  • Ojen Kumar Narain

摘要

The application of a Bregman subgradient extragradient algorithm to pseudomonotone equilibrium and fixed points problems associated with quasi-Bregman nonexpansive mappings is considered. We incorporate a Bregman distance framework and an inertial extrapolation technique to approximate a common solution to both the equilibrium problem and the fixed points of quasi-Bregman nonexpansive mappings within a reflexive Banach space. In addition, we introduce a regulating parameter, denoted by \(\eta \) η , to regulate and enhance the step size of the algorithm such that the cost operator does not rely on the Lipschitz constant. We verify the accuracy and effectiveness of our approach with two numerical examples. We note that the incorporation of our parameter \(\eta \) η improves the convergence rate compared to other algorithms. Also, we observed that the smaller the value of \(\eta \) η , the faster the convergence. These results demonstrate the effectiveness of our algorithm and provide contributions that advance existing knowledge in this research domain.