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<p>Several results on iterative methods for equilibrium problems have been proposed and studied in the literature. Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator. Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature. In this paper, we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity. We propose two weakly convergent iterative algorithms and one strongly convergent algorithm. We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction. Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.</p>

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Three inertial acceleration algorithms for solving non-monotone equilibrium problems in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Yonghong Yao,
  • Olaniyi S. Iyiola,
  • Yekini Shehu

摘要

Several results on iterative methods for equilibrium problems have been proposed and studied in the literature. Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator. Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature. In this paper, we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity. We propose two weakly convergent iterative algorithms and one strongly convergent algorithm. We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction. Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.