Abstract We study the proximal point method for solving quasi-equilibrium problems in Banach spaces, which generalizes the proximal point method for equilibrium problems and quasi-variational inequalities. We propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the quasi-equilibrium problem, under standard assumptions on the problem without assuming neither pseudo-monotonicity nor any weak continuity assumption of the bifunction in its arguments that in many well-known methods have been used. Also, we show that the boundedness of the generated sequences implies that the solution set of the quasi-equilibrium problem is nonempty and prove the strong convergence of the generated sequence to a solution of the quasi-equilibrium problem when these conditions are satisfied.

中文翻译：

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Banach空间中拟平衡问题的近点法

摘要 我们研究了求解Banach空间中拟平衡问题的近点法，它推广了求解平衡问题和拟变分不等式的近点法。我们提出了一个正则化程序，它确保生成的序列强收敛到准平衡问题的解决方案，在问题的标准假设下，既不假设双函数的伪单调性，也不假设双函数的任何弱连续性假设在许多井中- 已使用已知方法。此外，我们证明了生成序列的有界性意味着准平衡问题的解集是非空的，并证明了当满足这些条件时生成序列对准平衡问题的解的强收敛性。