Over the past decades, the split inverse problem has been widely studied, and one of the objectives of those researches is to invent some efficient algorithms for approximating solutions. Most of those algorithms depend on the norms of bounded linear operators; however, the calculation of the operator norms is not an easy task in general practice. In this article, we study and investigate the split fixed point problem for multi-valued mappings in Hilbert spaces. We introduce a self-adaptive algorithm without prior knowledge of the operator norm for two demicontractive multi-valued mappings, and establish a strong convergence theorem of the proposed method under some suitable conditions. Our main result in this paper generalizes and improves many results in the literature.

在过去的几十年里，分裂逆问题得到了广泛的研究，这些研究的目标之一是发明一些有效的算法来逼近解。大多数这些算法依赖于有界线性算子的范数；然而，算子范数的计算在一般实践中并不是一件容易的事。在本文中，我们研究和研究了希尔伯特空间中多值映射的分裂不动点问题。我们引入了一种自适应算法，无需事先了解两个非收缩多值映射的算子范数，并在某些合适的条件下建立了所提出方法的强收敛定理。我们在本文中的主要结果概括并改进了文献中的许多结果。