In this paper, we introduce a self-adaptive subgradient extragradient method for finding a common element in the solution set of a pseudomonotone equilibrium problem and set of fixed points of a quasi-ϕ-nonexpansive mapping in 2-uniformly convex and uniformly smooth Banach spaces. The stepsize of the algorithm is selected self-adaptively which helps to prevent the necessity for prior estimates of the Lipschitz-like constants of the bifunction. A strong convergence result is proved under some mild conditions and some applications to Nash equilibrium problem and contact problem are presented to show the applicability of the result. Furthermore, some numerical examples are given to illustrate the efficiency and accuracy of the proposed method by comparing with other related methods in the literature.

在本文中，我们介绍了一种自适应次梯度外梯度方法，用于在伪单调平衡问题的解集和2-一致凸和一致光滑 Banach 空间中的拟非膨胀映射的不动点集中寻找公共元素. 该算法的步长是自适应选择的，这有助于避免事先估计双函数的 Lipschitz 样常数的必要性。在一些温和的条件下证明了强收敛性结果，并给出了一些在纳什均衡问题和接触问题上的应用，以表明结果的适用性。此外，通过与文献中其他相关方法的比较，给出了一些数值例子来说明所提方法的效率和准确性。