In this paper, we introduce an explicit subgradient extragradient algorithm for solving equilibrium problem with a bifunction satisfying pseudomonotone and Lipschitz-like condition in a 2-uniformly convex and uniformly smooth Banach space. We also defined a new self-adaptive stepsize rule and prove a convergence result for solving the equilibrium problem without any prior estimate of the Lipschitz-like constants of the bifunction. Furthermore, we provide some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. This result improves and extends many recent results in this direction in the literature.

中文翻译：

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Banach空间中伪单调平衡问题的具有自适应步长的显式次梯度超梯度算法

在本文中，我们介绍了一种显式次梯度超梯度算法，用于求解在两个一致凸且一致光滑的Banach空间中具有伪单调和类似Lipschitz条件的双函数的平衡问题。我们还定义了一个新的自适应逐步调整规则，并证明了求解平衡问题的收敛结果，而无需事先估计双功能的Lipschitz样常数。此外，我们提供了一些数值示例来说明所提出算法的效率和准确性。该结果改进并扩展了文献中朝该方向的许多最新结果。