Abstract In this paper, the notion of generalized split feasibility problem (GSFP) is studied in p-uniformly convex Banach spaces. Some special cases of the GSFP are highlighted. A self-adaptive step-size iterative algorithm which converges strongly to solution of the GSFP is proved. The implementation of the method is demonstrated with two numerical examples. Our method does not require prior information of operator norms. Our results extend, improve and enrich recently announced related results in the literature.

中文翻译：

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Banach空间中多值Bregman拟非扩张映射的广义分裂可行性问题

摘要 本文研究了p-均匀凸Banach空间中的广义分裂可行性问题(GSFP)的概念。突出显示了 GSFP 的一些特殊情况。证明了一种自适应步长迭代算法，该算法对GSFP的解有很强的收敛性。用两个数值例子说明了该方法的实现。我们的方法不需要操作员规范的先验信息。我们的结果扩展、改进和丰富了最近在文献中公布的相关结果。