双曲空间中广义非扩张映射的一个修正迭代过程的收敛性定理

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2020-12-01 DOI:10.2748/tmj.20191210

Preeyalak Chuadchawna, A. Farajzadeh, A. Kaewcharoen

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引用次数: 2

摘要

本文给出了双曲空间框架下有限族映射的一种改进的Picard-Mann混合迭代过程。在此基础上，我们进一步建立了由一个改进的Picard-Mann混合迭代过程生成的序列的$\Delta$收敛性和强收敛性结果，该序列包含满足条件$(E)$的映射，该映射在Ritika和Khan[19]的双曲空间设置下比在CAT(0)空间设置下的一个映射更一般。我们的结果是Ritika和Khan[19]结果的推广和改进。此外，在数值算例中，我们还举例来支持我们的主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Convergence theorems of a modified iteration process for generalized nonexpansive mappings in hyperbolic spaces

In this paper, we introduce a modified Picard-Mann hybrid iterative process for a finite family of mappings in the framework of hyperbolic spaces. Furthermore, we establish $\Delta$-convergence and strong convergence results for a sequence generated by a modified Picard-Mann hybrid iterative process involving mappings satisfying the condition $(E)$ in the setting of hyperbolic spaces which more general than one mapping in the setting of CAT(0) spaces in Ritika and Khan [19]. Our results are the extension and improvement of the results in Ritika and Khan [19]. Moreover, in the numerical example we also illustrate an example for supporting our main result.

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