This paper aims to study the stability in the sense of Hausdorff continuity of solution maps to equilibrium problems without assuming the solid condition of ordered cones. We first propose a generalized concavity of set-valued maps and discuss its relation with the existing concepts. Then, by using the above property and the continuity of the objective function, sufficient conditions for the Hausdorff continuity of solution maps to scalar equilibrium problems are established. Finally, we utilize the oriented distance function to obtain the Hausdorff continuity of solution maps to set-valued equilibrium problems via the corresponding results of the scalar equilibrium problems.

中文翻译：

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解的豪斯多夫连续性通过定向距离函数映射到平衡问题

本文旨在研究平衡问题解映射的豪斯多夫连续性意义上的稳定性，而不假设有序锥体的固体条件。我们首先提出集值映射的广义凹性并讨论其与现有概念的关系。然后，利用上述性质和目标函数的连续性，建立了标量平衡问题解映射的豪斯多夫连续性的充分条件。最后，利用定向距离函数，通过标量平衡问题的相应结果，获得集值平衡问题解图的豪斯多夫连续性。