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巴拿赫空间中单调映射零点的粘性迭代算法。

Viscosity iterative algorithm for the zero point of monotone mappings in Banach spaces.

作者信息

Tang Yan

机构信息

College of Mathematics and Statistics, Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing Technology and Business University, Chongqing, China.

出版信息

J Inequal Appl. 2018;2018(1):254. doi: 10.1186/s13660-018-1845-1. Epub 2018 Sep 21.

DOI:10.1186/s13660-018-1845-1
PMID:30839705
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6154085/
Abstract

Inspired by the work of Zegeye (J. Math. Anal. Appl. 343:663-671, 2008) and the recent papers of Chidume et al. (Fixed Point Theory Appl. 2016:97, 2016; Br. J. Math. Comput. Sci. 18:1-14, 2016), we devise a viscosity iterative algorithm without involving the resolvent operator for approximating the zero of a monotone mapping in the setting of uniformly convex Banach spaces. Under concise parameter conditions we establish strong convergence of the proposed algorithm. Moreover, applications to constrained convex minimization problems and solution of Hammerstein integral equations are included. Finally, the performances and computational examples and a comparison with related algorithms are presented to illustrate the efficiency and applicability of our new algorithm.

摘要

受泽盖耶（《数学分析与应用杂志》343:663 - 671，2008年）的工作以及奇杜梅等人近期论文（《不动点理论及其应用》2016:97，2016年；《英国数学与计算机科学杂志》18:1 - 14，2016年）的启发，我们设计了一种不涉及预解算子的粘性迭代算法，用于在一致凸巴拿赫空间的背景下逼近单调映射的零点。在简洁的参数条件下，我们建立了所提算法的强收敛性。此外，还包括对约束凸最小化问题的应用以及哈默斯坦积分方程的求解。最后，给出了性能、计算示例以及与相关算法的比较，以说明我们新算法的效率和适用性。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/110f/6154085/901a8f480e1e/13660_2018_1845_Fig10_HTML.jpg
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本文引用的文献

1
Constructive techniques for zeros of monotone mappings in certain Banach spaces.某些巴拿赫空间中单调映射零点的构造性技术。
Springerplus. 2015 Jul 28;4:383. doi: 10.1186/s40064-015-1169-2. eCollection 2015.