In this paper, we study the class of further generalized hybrid mappings due to Khan (Fixed Point Theory Appl. 2018:8, 2018) in the setting of Hadamard spaces. We prove a demiclosed principle for such mappings in Hadamard spaces. Furthermore, we also prove the Δ-convergence of the sequence generated by the S-iteration process for finding attractive points of further generalized hybrid mappings in Hadamard spaces satisfying the $(\mathbb{S})$ property and the $(\overline{Q_{4}})$ condition. Moreover, we provide a numerical example to illustrate the convergence behavior of the studied iteration and numerically compare the convergence of the studied iteration scheme with the existing schemes. Our results extend some known results which appeared in the literature.

中文翻译：

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Hadamard空间中进一步广义混合映射的吸引点的迭代逼近

在本文中，我们研究在Hadamard空间中由于Khan（Fixed Point Theory Appl.2018：8，2018）而产生的进一步广义混合映射的类。我们证明了Hadamard空间中此类映射的非封闭原理。此外，我们还证明了由S迭代过程生成的序列的Δ收敛性，用于在Hadamard空间中找到满足$（\ mathbb {S}）$属性和$（\ overline { Q_ {4}}）$条件。此外，我们提供了一个数值示例来说明所研究迭代的收敛行为，并将所研究迭代方案与现有方案的收敛进行数值比较。我们的结果扩展了文献中出现的一些已知结果。