In this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

中文翻译：

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Brezis 伪单调双函数和通过惩罚的准平衡问题

在本文中，我们在所涉及函数的 Brezis 伪单调性假设下研究了真实 Banach 空间中的准平衡问题。为了在弱矫顽力条件下建立存在结果，我们用一系列受惩罚的通常平衡问题替换了准平衡问题。为了处理非紧凑框架，我们应用了惩罚方法的正则化版本。还考虑了集合值准变分不等式的特殊情况。