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关于希尔伯特空间中混合型多值映射的分裂混合平衡问题与不动点问题的求解

On solving split mixed equilibrium problems and fixed point problems of hybrid-type multivalued mappings in Hilbert spaces.

作者信息

Onjai-Uea Nawitcha, Phuengrattana Withun

机构信息

Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University, Nakhon Pathom, 73000 Thailand.

Research Center for Pure and Applied Mathematics, Research and Development Institute, Nakhon Pathom Rajabhat University, Nakhon Pathom, 73000 Thailand.

出版信息

J Inequal Appl. 2017;2017(1):137. doi: 10.1186/s13660-017-1416-x. Epub 2017 Jun 15.

DOI:10.1186/s13660-017-1416-x
PMID:28680240
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5487942/
Abstract

In this paper, we introduce and study iterative algorithms for solving split mixed equilibrium problems and fixed point problems of -hybrid multivalued mappings in real Hilbert spaces and prove that the proposed iterative algorithm converges weakly to a common solution of the considered problems. We also provide an example to illustrate the convergence behavior of the proposed iteration process.

摘要

在本文中,我们介绍并研究了用于求解实希尔伯特空间中分裂混合均衡问题和 - 混合多值映射不动点问题的迭代算法,并证明了所提出的迭代算法弱收敛到所考虑问题的一个公共解。我们还给出一个例子来说明所提出迭代过程的收敛行为。

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本文引用的文献

1
Strong convergence algorithm for split equilibrium problems and hierarchical fixed point problems.分裂均衡问题和分层不动点问题的强收敛算法
ScientificWorldJournal. 2014 Feb 20;2014:390956. doi: 10.1155/2014/390956. eCollection 2014.
2
A unified approach for inversion problems in intensity-modulated radiation therapy.调强放射治疗中反演问题的统一方法。
Phys Med Biol. 2006 May 21;51(10):2353-65. doi: 10.1088/0031-9155/51/10/001. Epub 2006 Apr 26.