This paper provides iterative construction of a common solution associated with a class of equilibrium problems and split convex feasibility problems. In particular, we are interested in the equilibrium problems defined with respect to the pseudomonotone and Lipschitz-type continuous equilibrium problem together with the generalized split null point problems in real Hilbert spaces. We propose an iterative algorithm that combines the hybrid extragradient method with the inertial acceleration method. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under suitable set of constraints and numerical results concerning the viability of the proposed algorithm with respect to various real-world applications.

本文提供了与一类平衡问题和分裂凸可行性问题相关的通用解决方案的迭代构造。特别是，我们对假单调和 Lipschitz 型连续平衡问题定义的平衡问题以及真实希尔伯特空间中的广义分裂零点问题感兴趣。我们提出了一种将混合外梯度法与惯性加速法相结合的迭代算法。对所提出算法的分析包括关于在适当的约束条件下强收敛的理论结果和关于所提出算法在各种实际应用中的可行性的数值结果。