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<p>In this article, a reflected-proximal method for solving equilibrium problems is proposed. Using this method, weak and strong convergence results together with the rate of convergence are obtained under certain assumptions. The method requires only one computation of the proximal per iteration thereby making it less computationally expensive. Furthermore, the case when the feasible set is the set of fixed points of enriched nonexpansive mappings is considered for the reflected-proximal and non-reflected proximals. Finally, substantial results for a variational inequality problem are obtained as consequences of the main results. The results not only contribute theoretically but also discuss the practical effectiveness of the methods, as evidenced by illustrative examples.</p>

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Proximal methods for equilibrium problems over the set of fixed points of enriched nonexpansive mappings

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Natthaya Boonyam,
  • Sani Salisu,
  • Vasile Berinde,
  • Poom Kumam

摘要

In this article, a reflected-proximal method for solving equilibrium problems is proposed. Using this method, weak and strong convergence results together with the rate of convergence are obtained under certain assumptions. The method requires only one computation of the proximal per iteration thereby making it less computationally expensive. Furthermore, the case when the feasible set is the set of fixed points of enriched nonexpansive mappings is considered for the reflected-proximal and non-reflected proximals. Finally, substantial results for a variational inequality problem are obtained as consequences of the main results. The results not only contribute theoretically but also discuss the practical effectiveness of the methods, as evidenced by illustrative examples.