Our main aim is to introduce an iterative algorithm for the approximation of a common solution to a splitequality problem for finite families of variational inequalities and the split equality fixed-point problem. By using our iterative algorithm, we state and prove a strong convergence theorem for the approximation of an element in the intersection of the set of solutions of the split-equality problem for finite families of variational inequalities and the set of solutions of the split equality fixed-point problem for countable families of multivalued type-one mappings of the demicontractive type. Finally, we apply our result to study related problems. Our result supplements and extends some recent results available from the literature.

中文翻译：

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变分不等式系统和多集分裂等式不动点问题的可数族的多值第一类映射的半收缩类型

我们的主要目的是引入一种迭代算法，用于逼近有限变分不等式的分裂等式问题和分裂等式不动点问题的通用解。通过使用我们的迭代算法，我们陈述并证明了一个强收敛定理，用于逼近有限变分不等式的分裂等式问题的解集与固定分裂等式的解集的交集解压缩类型的多值类型一映射的可数族的点问题。最后，我们将我们的结果应用于研究相关问题。我们的结果补充和扩展了一些从文献中获得的最新结果。