We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.

中文翻译：

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关于可数非扩张多值映射族的分裂广义均衡问题和不动点问题

我们考虑了实希尔伯特空间中可数非扩张多值映射族的分裂广义均衡问题和不动点问题。然后，使用收缩投影方法，我们证明了一个强的收敛定理，可以找到所考虑问题的通用解。数值例子说明了收敛结果。我们的结果改进并扩展了文献中的相应结果。