求解半压缩映射分裂公共不动点问题的新型平均型算法
New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings
AI总结：
本文通过在已有迭代算法中引入平均项，构造求解半压缩映射分裂公共不动点问题的新平均迭代算法，并在实 Hilbert 空间中证明其弱、强收敛性。
摘要：
本文提出了新的平均迭代算法，旨在求解半压缩映射类别中的分裂公共不动点问题。这些算法是通过在 Li 与 He 于《J. Inequal. Appl.》第131卷（2015年）第1–12页发表的论文《A new iterative algorithm for split solution problems of quasi-nonexpansive mappings》中所用算法里插入一个平均项而得到的；该文算法用于求解同一问题，但针对的是准非扩张映射类别，而准非扩张映射是半压缩映射的一个子类。从根本上说，我们的研究基于借助平均映射将半压缩算子嵌入到准非扩张算子类别中。对于所考虑的算法，我们在实 Hilbert 空间框架下证明了弱收敛和强收敛定理，并通过实例表明，我们的结果是对文献中已有结果的有效推广。
英文摘要：
In this paper we propose new averaged iterative algorithms designed for solving a split common fixed-point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings {\it J. Inequal. Appl.} {\bf 131} (2015), 1--12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space and also provide examples to show that our results are effective generalizations of existing results in literature.
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