Motivated by the work of D.V. Hieu and J.-J. Strodiot [Strong convergence theorems for equilibrium problems and fixed point problems in Banach spaces, J. Fixed Point Theory Appl., (2018), 20:131], we introduce a new projected subgradient method for solving pseudomonotone equilibrium and fixed point problem in Banach spaces. The main iterative steps in the proposed method use a projection method and do not require any Lipschitz-like condition on the equilibrium bifunction. A strong convergence result is proved under mild conditions and we applied our algorithm to solving pseudomonotone variational inequalities in Banach spaces. Also, we provide some numerical examples to illustrate the performance of the proposed method and compare it with other methods in the literature.

受DV Hieu和J.-J. Strodiot [Banach空间中平衡问题和不动点问题的强收敛定理，J。不动点理论应用，（2018），20：131]，我们引入了一种新的投影次梯度法来解决Banach中的伪单调平衡和不动点问题空格。所提出的方法中的主要迭代步骤使用投影方法，并且在平衡双功能上不需要任何类似于Lipschitz的条件。证明了在温和条件下的强收敛结果，并且我们将我们的算法应用于解决Banach空间中的伪单调变分不等式。此外，我们提供了一些数值示例来说明该方法的性能，并将其与文献中的其他方法进行比较。