In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of A. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.

中文翻译：

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求解Banach空间中修改的分裂可行性问题的强收敛惯性迭代算法。

在本文中，我们针对Banach空间中具有最大单调算子和不动点问题的特殊分裂可行性问题提出了一种迭代方案。该算法使用惯性技术来实现该问题的Halpern迭代。在相关映射的单调性的一些温和假设下，我们建立了算法生成的序列的强收敛性，该算法不需要A的谱半径。最后，通过算例说明了算法的有效性。