In this paper, we are concern with the classical equilibrium problem in real Hilbert spaces and introduce two new extragradient variants for it. By taking into account several fixed point theory techniques, we obtain simple structure methods that converge strongly and hence demonstrate the theoretical advantage of our methods. Moreover, our convergence assumptions are weaker than those assumed in related works in the literature. Primary numerical examples with comparisons illustrate the behaviour of our proposed scheme and show its advantages.

中文翻译：

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解决平衡问题的两种新的超梯度方法

在本文中，我们关注实希尔伯特空间中的经典平衡问题，并为其引入两个新的超梯度变体。通过考虑几种定点理论技术，我们获得了可以很强地收敛的简单结构方法，从而证明了我们方法的理论优势。而且，我们的收敛性假设要弱于相关文献中的假设。带有比较的主要数值示例说明了我们提出的方案的行为并显示了其优点。