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<p>In this paper, we present a novel algorithm designed to approximate a common solution for both a pseudomonotone equilibrium problem and the common fixed point problem associated with a finite family of generalized demimetric mappings within a real Hilbert space. Our proposed algorithm employs an inertial approach that integrates a correction term and leverages the subgradient extragradient method. We introduce an innovative step size rule that operates independently of the Lipschitz-type constants associated with the bifunction. Under mild assumptions, we establish the strong convergence of our algorithm to a common solution for the problems under consideration, which corresponds to a unique solution of a specific hierarchical variational inequality defined on their common solution set. Finally, we illustrate the advantages and efficiency of the proposed algorithm through a series of numerical examples.</p>

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A novel algorithm for approximating common solution of pseudomonotone equilibrium problem and common fixed point problem

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Mohammad Eslamian,
  • Ahmad Kamandi

摘要

In this paper, we present a novel algorithm designed to approximate a common solution for both a pseudomonotone equilibrium problem and the common fixed point problem associated with a finite family of generalized demimetric mappings within a real Hilbert space. Our proposed algorithm employs an inertial approach that integrates a correction term and leverages the subgradient extragradient method. We introduce an innovative step size rule that operates independently of the Lipschitz-type constants associated with the bifunction. Under mild assumptions, we establish the strong convergence of our algorithm to a common solution for the problems under consideration, which corresponds to a unique solution of a specific hierarchical variational inequality defined on their common solution set. Finally, we illustrate the advantages and efficiency of the proposed algorithm through a series of numerical examples.