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<p>Our goal in this paper, is to establish existence theorems for the solutions of equilibrium problems when the bifunction involved is defined on the Cartesian product of two distinct sets. Our approach is based on an intersection theorem due to Greco [<CitationRef CitationID="CR24">24</CitationRef>]. The results concerning equilibrium problems are then used to establish criteria for the existence of solutions to the Minty and Stampacchia variational inequalities for set-valued mappings that do not satisfy any continuity conditions. The quasi-equilibrium problems and quasi-variational inequalities are considered at the end of the paper.</p>

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Equilibrium problems: existence criteria and applications

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Mircea Balaj

摘要

Our goal in this paper, is to establish existence theorems for the solutions of equilibrium problems when the bifunction involved is defined on the Cartesian product of two distinct sets. Our approach is based on an intersection theorem due to Greco [24]. The results concerning equilibrium problems are then used to establish criteria for the existence of solutions to the Minty and Stampacchia variational inequalities for set-valued mappings that do not satisfy any continuity conditions. The quasi-equilibrium problems and quasi-variational inequalities are considered at the end of the paper.