CAT(0) 空间中准无穷多值映射可数族共同定点的迭代算法

IF 1.9 4区 数学 Q1 MATHEMATICS
Sani Salisu, Ma’aruf Shehu Minjibir
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引用次数: 0

摘要

在本文中,我们提出了一种准无穷映射可数族共同定点的迭代方案。该方案以大地平均技术为基础,只涉及选定的元素,计算成本较低。在每次迭代时,该方案只需要大地线段,而不需要进一步的技术循环或优化。在不同的温和条件下,我们建立了所提方案到所需点的收敛性和强收敛性结果(假设存在)。值得注意的是,所考虑的映射不需要有紧凑的图像,以及其他宽松的条件。此外,所进行的数值实验表明了该方案的鲁棒性。本文提出的结果不仅丰富了现有的相关文献,还为之前的研究提供了宝贵的补充。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Iterative algorithms for common fixed points of a countable family of quasi-nonexpansive multivalued mappings in CAT(0) spaces

Iterative algorithms for common fixed points of a countable family of quasi-nonexpansive multivalued mappings in CAT(0) spaces

In this paper, we propose an iterative scheme for a common fixed point of a countable family of quasi-nonexpansive mappings. The scheme is computationally less expensive, built on a geodesic averaging technique involving only selected elements. At each iteration, the scheme requires only geodesic segments and no further technical looping or optimizations. Under distinct mild conditions, we establish both \(\triangle\)-convergence and strong convergence result for the proposed scheme to the required point, assuming existence. Notably, the considered mappings need not have compact images, among other relaxed conditions. Additionally, numerical experiments conducted show the robustness of the scheme. The results presented in this paper, not only enhances the existing related literature, but also offers valuable complements to previous studies.

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来源期刊
CiteScore
4.20
自引率
5.00%
发文量
44
期刊介绍: Mathematical Sciences is an international journal publishing high quality peer-reviewed original research articles that demonstrate the interaction between various disciplines of theoretical and applied mathematics. Subject areas include numerical analysis, numerical statistics, optimization, operational research, signal analysis, wavelets, image processing, fuzzy sets, spline, stochastic analysis, integral equation, differential equation, partial differential equation and combinations of the above.
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