The paper concerns with two new schemes for approximating solutions of equilibrium problems involving monotone and Lipschitz-type bifunctions in Hilbert spaces. We describe how to incorporate the two-step proximal-like method (modified extragradient method) with the regularization technique and then we propose two iterative regularization algorithms for solving equilibrium problems. Unlike the viscosity-like methods, we establish the strong convergence of the new algorithms based on the regularization. The first algorithm is designed to work with the prior knowledge of Lipschitz-type constants of bifunction while the second one, with a simple stepsize rule, is done without this requirement. In order to illustrate the effectiveness and the convergence of the algorithms, we provide several numerical experiments in comparisons with other well known algorithms, which show that our new algorithms are effective for solving equilibrium problems.wi

该论文涉及两种新方案，用于逼近 Hilbert 空间中涉及单调和 Lipschitz 型双函数的平衡问题的解。我们描述了如何将两步近端方法（改进的超梯度方法）与正则化技术相结合，然后我们提出了两种迭代正则化算法来解决平衡问题。与粘性类方法不同，我们建立了基于正则化的新算法的强收敛性。第一个算法设计用于使用双函数的 Lipschitz 型常数的先验知识，而第二个算法具有简单的步长规则，无需此要求即可完成。为了说明算法的有效性和收敛性，