Modified Halpern Iteration and Viscosity Approximation Methods for Split Feasibility Problems in Hilbert Spaces
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摘要: 在无限维Hilbert空间中,提出了求解分裂可行性问题(SFP)的改进Halpern迭代和黏性逼近算法,证明了当参数满足一定条件时,由给定算法生成的序列强收敛到分裂可行性问题的一个解.这些结论推广了Deepho和Kumam近年来的一些结果
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关键词:
- 分裂可行性问题 /
- 改进Mann迭代和黏性逼近方法 /
- 强收敛 /
- Hilbert空间
Abstract: In infinitedimensional Hilbert spaces, the modified Halpern iteration and viscosity approximation methods for solving the split feasibility problems (SFPs) were proposed. When the parameters satisfy certain conditions, it is proved that the sequences generated with the proposed algorithms converge strongly to a solution to the split feasibility problem. The main findings improve and extend some recent results by Deepho and Kumam. -
[1] Censor Y, Bortfeld T, Martin B, et al. A unified approach for inversion problems in intensity-modulated radiation therapy[J]. Physics in Medicine and Biology,2006,51(10): 2253-2365. [2] Censor Y, Elfving T, Kopf N, et al. The multiple-sets split feasibility problem and its applications for inverse problems[J]. Inverse Problems,2005,21(6): 2071-2084. [3] Censor Y, Motiva A, Segal A. Perturbed projections and subgradient projections for the multiple-sets split feasibility problem[J]. Journal of Mathematical Analysis and Applications,2007,327(2): 1244-1256. [4] Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space[J]. Numerical Algorithms,1994,8(2): 221-239. [5] XU Hong-kun. Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces[J]. Inverse Problems,2010,26(10): 1-17. [6] TANG Yu-chao, LIU Li-wei. Iterative methods of strong convergence theorems for the split feasibility problem in Hilbert spaces[J]. Journal of Inequalities and Applications,2016(1): 2-14. doi: 10.1186/s13660-016-1228-4. [7] XU Hong-kun. A variable Krasnosel’skiǐ-Mann algorithm and the multiple-set split feasibility problem[J]. Inverse Problems,2006,22(6): 2021-2034. [8] YANG Qing-zhi. The relaxed CQ algorithm solving the split feasibility problem[J]. Inverse Problems,2004,20(4): 1261-1266. [9] YANG Qing-zhi, ZHAO Jin-ling. Generalized KM-theorems and their applications[J]. Inverse Problems,2006,22(3): 833-844. [10] Byrne C. Iterative oblique projection onto convex sets and the split feasibility problem[J]. Inverse Problems,2002,18(2): 441-453. [11] XU Hong-kun. Viscosity approximation methods for nonexpansive mappings[J]. Journal of Mathematical Analysis and Applications,2004,298(1): 279-291. [12] Deepho J, Kumam P. A viscosity approximation method for the split feasibility problems[J]. Transactions on Engineering Technologies,2014,2(6): 69-77. [13] WANG Feng-hui, XU Hong-kun. Approximating curve and strong convergence of the CQ algorithm for the split feasibility problem[J]. Journal of Inequalities and Applications,2010(1): 1-13. doi: 10.1155/2010/102085. [14] XU Hong-kun. Iterative algorithms for nonlinear operators[J]. Journal of the London Mathematical Society,2002,66(1): 240-256. [15] Goebel K, Kirk W A. Topics in Metric Fixed Point Theory [M]. Cambridge: Cambridge University Press, 1990.
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